System and method for building heating-modification-based gross energy load modeling with the aid of a digital computer

ABSTRACT

Gross energy load can be determined by combining periodic net load statistics, such as provided by a power utility or energy agency, with on-site power generation, such as photovoltaic power generation, as produced over the same time period. The gross energy load provides an indication upon which other types of energy investment choices can be evaluated. These choices can include traditional energy efficiencies, such as implementing electrical efficiency measures, which includes cutting down on and avoiding wasteful energy use and switching to energy efficient fixtures, and improving the thermal efficiency and performance of a building. The choices can also include non-traditional energy efficiencies, such as replacing a gasoline-powered vehicle with an electric vehicle, fuel switching from a water heater fueled by natural gas to a heat pump water heater, and fuel switching from space heating fueled by natural gas to a heat pump space heater.

FIELD

This application relates in general to energy conservation and planningand, in particular, to a system and method for buildingheating-modification-based gross energy load modification modeling withthe aid of a digital computer.

BACKGROUND

Concern has been growing in recent days over energy consumption in theUnited States and abroad. The cost of energy has steadily risen as powerutilities try to cope with continually growing demand, increasing fuelprices, and stricter regulatory mandates. Power utilities must alsomaintain existing infrastructure, while simultaneously finding ways toadd more generation capacity to meet future needs, both of which add tothe cost of energy. Moreover, burgeoning energy consumption continues toimpact the environment and deplete natural resources.

Such concerns underlie industry and governmental efforts to strive for amore efficient balance between energy consumption and supply. Forexample, the Zero Net Energy (ZNE) initiative, backed by the U.S.Department of Energy, promotes the goal of balancing the total energyused by a building annually with the total energy generated on-site. InCalifornia, the 2013 Integrated Energy Policy Report (IEPR) builds onearlier ZNE goals by mandating that all new residential and commercialconstruction be ZNE-compliant, respectively, by 2020 and 2030. The IEPRdefines a building as consuming zero net energy if the net amount ofenergy produced by renewable energy resources on-site roughly equals thevalue of the energy consumed by the building annually.

As the principal source of energy for most consumers, power utilitiesand energy agencies are at the forefront of energy efficiencyinitiatives, such as ZNE. These organizations often reach out to theircustomers through educational and incentive programs that are frequentlypitched as ways to lower monthly energy bills. Typically, they urgeenergy conservation by cutting down on and avoiding wasteful energy useand by switching to energy efficient fixtures. They also often promotethe on-site adoption of alternative sources of renewable energy.

Lowering monthly utility bills, however, is just a part of the broaderproblem of balancing energy consumption against supply. The averageconsumer continually consumes energy, whether electricity, natural gas,or other source; electricity may be purchased from the power utility or,less frequently, generated on-site. At home, energy may be used forspace heating and cooling, lighting, cooking, powering appliances andelectrical devices, heating water, and doing laundry. Energy may also beconsumed for personal transportation needs, whether by privateconveyance or public mass transit.

To raise energy awareness, power utilities often provide periodic energyconsumption statistics that are gathered through the use of smart powermeters or similar technologies. Such statistics, though, invariablyreflect net power consumption based only upon the energy purchased fromthe power utility. Energy generated (and consumed) on-site is notincluded, as utilities currently lack practicable ways of gathering andaggregating on-site energy production and consumption values into theirown power consumption statistics, in part, due to the vagaries inend-consumer equipment and energy consumption patterns.

Utility-provided net power consumption statistics can mask the overallefficiency of a building, particularly where on-site power generationand consumption significantly contributes to gross energy load.Effective energy balancing requires decreasing the amount of energyconsumed and generating energy on-site. Performing both of these stepsis crucial to lowering gross energy load, yet determining howefficiently energy is consumed is often skipped when a switch to analternative energy source is made first. For instance, the installationof a photovoltaic (PV) system on a private residence frequently leads aconsumer to (erroneously) conclude that further efforts at increasingenergy efficiency are no longer necessary or worthwhile. The immediacyof lower monthly utility bills and favorable net power consumptionstatistics can reinforce this misperception.

Therefore, a need remains for an approach to empowering consumers,particularly residential customers, with full knowledge of actual grossenergy consumption and an understanding what options and alternativeswork best for their energy needs, especially in situations whererenewable energy sources are already in place.

SUMMARY

The percentage of the total fuel purchased for space heating purposescan be fractionally inferred by evaluating annual fuel purchase data. Anaverage of monthly fuel purchases during non-heating season months isfirst calculated. The fuel purchases for each month is then compared tothe average monthly fuel purchase, where the lesser of the average andthat month's fuel purchase are added to a running total of annual spaceheating fuel purchases.

In addition, the overall thermal performance of a building UA^(Total)can be empirically estimated through a short-duration controlled test.Preferably, the controlled test is performed at night during the winter.A heating source, such as a furnace, is turned off after the indoortemperature has stabilized. After an extended period, such as 12 hours,the heating source is turned back on for a brief period, such as onehour, then turned back off. The indoor temperature is allowed tostabilize. The energy consumed within the building during the testperiod is assumed to equal internal heat gains. Overall thermalperformance is estimated by balancing the heat gained with the heat lostduring the test period.

Furthermore, potential energy investment scenarios can be evaluated.Energy performance specifications and prices for both existing andproposed energy-related equipment are selected, from which an initialcapital cost is determined. The equipment selections are combined withcurrent fuel consumption data, thermal characteristics of the building,and solar resource and other weather data to create an estimate of thefuel consumption of the proposed equipment. An electricity bill iscalculated for the proposed equipment, from which an annual cost isdetermined. The payback of the proposed energy investment is found bycomparing the initial and annual costs.

New energy investments specifically affecting building envelope, heatingsource, or heating delivery can be evaluated. Data that can include thepercentage of a fuel bill for fuel used for heating purposes, anexisting fuel bill, existing overall thermal properties UA^(Total) ofthe building, existing furnace efficiency, new furnace efficiency,existing delivery system efficiency, new delivery system efficiency,areas of building surfaces to be replaced or upgraded, existing U-valuesof thermal properties of building surfaces to be replaced or upgraded,new U-values of thermal properties of building surfaces to be replacedor upgraded, and number of air changes before and after energyinvestment are obtained. The impact of energy investments that affectheat transfer through the building envelope due to conduction, heatlosses due to infiltration, or both, are quantified by a comparativeanalysis of relative costs and effects on the building's thermalcharacteristics, both before and after the proposed changes.

Finally, gross energy load can be determined by combining periodic netload statistics, such as provided by a power utility or energy agency,with on-site power generation, such as photovoltaic power generation, asproduced over the same time period. The gross energy load provides anindication upon which other types of energy investment choices can beevaluated. These choices can include traditional energy efficiencies,such as implementing electrical efficiency measures, which includescutting down on and avoiding wasteful energy use and switching to energyefficient fixtures, and improving the thermal efficiency and performanceof a building. The choices can also include non-traditional energyefficiencies, such as replacing a gasoline-powered vehicle with anelectric vehicle, fuel switching from a water heater fueled by naturalgas to a heat pump water heater, and fuel switching from space heatingfueled by natural gas to a heat pump space heater.

In one embodiment, a system and method for buildingheating-modification-based gross energy load modification modeling withthe aid of a digital computer is provided. A gross energy loadassociated with a building is obtained by a computer, the computerincluding a processor and memory within which code for execution by theprocessor is stored, based on electricity provided to the building by apower utility and energy provided to the building by an on-siterenewable energy system. An overall thermal performance of the buildingis estimated by the computer by conducting an empirical test comprisingremotely controlling a heating source inside the building. An effect ofone or more changes to the overall thermal performance of the buildingon the gross energy load is modeled by the computer, includingdetermining a characteristic of a further heating source needed tosupply heat for space heating the building with the changed overallthermal performance, determining the characteristic of the furtherheating source including: obtaining a maximum amount of energy consumedin a single day during a time period for space heating in the building;determining at least one mathematical relationship between heatinglosses in the building before the changes are performed and heatinglosses estimated to be in the building after the changes are performed,and use the at least one mathematical relationship and the maximumamount of energy to determine a further maximum amount of the energythat would be needed in the building in a single day after the changesare performed; the characteristic is determined by the computer based onthe further maximum amount of the energy needed in the building afterthe changes are performed. A characteristic of a further renewableenergy system needed to power the further heating source is determinedby the computer using the characteristic of the heating source.

Still other embodiments will become readily apparent to those skilled inthe art from the following detailed description, wherein are describedembodiments by way of illustrating the best mode contemplated. As willbe realized, other and different embodiments are possible and theembodiments' several details are capable of modifications in variousobvious respects, all without departing from their spirit and the scope.Accordingly, the drawings and detailed description are to be regarded asillustrative in nature and not as restrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a Venn diagram showing, by way of example, a typicalconsumer's energy-related costs.

FIG. 2 is a flow diagram showing a function for fractionally inferringthe percentage of the total fuel purchased for space heating purposes,in accordance with one embodiment.

FIG. 3 is a graph depicting, by way of example, annual fuel purchases,including fuel purchased for space heating purposes.

FIG. 4 is a flow diagram showing method for empirically estimatingoverall thermal performance of a building through a short-durationcontrolled test, in accordance with one embodiment.

FIG. 5 a graph depicting, by way of example, the controlled,short-duration test of FIG. 4 .

FIG. 6 is a graph depicting, by way of example, the controlled,short-duration test of FIG. 4 for a different day.

FIG. 7 is a screen shot showing, by way of example, an analysis ofenergy investment choices.

FIG. 8 is a process flow diagram showing a computer-implemented methodfor evaluating potential energy investment scenarios from a user'sperspective, in accordance with one embodiment.

FIG. 9 is a detail of the graphical user interface of FIG. 7 showing, byway of example, an annotated graph of hourly electricity consumption.

FIG. 10 is a graph showing, by way of example, monthly net energyconsumption statistics.

FIG. 11 is a graph showing, by way of example, average daily net energyconsumption statistics, including on-site photovoltaic power generation.

FIG. 12 is a graph showing, by way of example, average daily grossenergy consumption statistics, excluding on-site photovoltaic powergeneration.

FIG. 13 is a graph showing, by way of example, average daily grossenergy consumption statistics, excluding on-site photovoltaic powergeneration with light emitting diode (LED) lighting fixtures andlighting usage reduction.

FIG. 14 is a graph showing, by way of example, average daily grossenergy consumption statistics, excluding on-site photovoltaic powergeneration with electric vehicle usage.

FIG. 15 is a graph showing, by way of example, average daily grossenergy consumption statistics, excluding on-site photovoltaic powergeneration with light emitting diode (LED) lighting fixtures, lightingusage reduction, and electric vehicle usage.

FIG. 16 is a graph showing, by way of example, average daily net energyconsumption statistics, including on-site photovoltaic power generationwith light emitting diode (LED) lighting fixtures, lighting usagereduction, and electric vehicle usage.

FIG. 17 is a process flow diagram showing a routine for estimating grossenergy load for use in the method of FIG. 8 .

FIG. 18 is a process flow diagram showing a routine for evaluatingpotential energy investment payback for use in the method of FIG. 8 .

FIG. 19 is a graph depicting, by way of example, assumed hourlydistribution factors, as used in the routine of FIG. 8 .

FIG. 20 is a flow diagram showing a computer-implemented method forevaluating potential energy investment scenarios specially affecting abuilding's envelope, heating source, or heating delivery, in accordancewith a further embodiment.

FIG. 21 is a process flow diagram showing a routine for selecting energyinvestment scenario parameters for use in the method of FIG. 20 .

FIG. 22 is a block diagram depicting, by way of example, annual energyconsumption by an average household in California with gasoline andnatural gas consumption expressed in kilowatt hours.

FIG. 23 is a block diagram depicting, by way of example, the annualenergy consumption of FIG. 22 reflecting energy efficiencies implementedthrough traditional methodologies.

FIG. 24 is a block diagram depicting, by way of example, the annualenergy consumption of FIG. 22 reflecting a switch to an electricvehicle.

FIG. 25 is a block diagram depicting, by way of example, the annualenergy consumption of FIG. 22 reflecting a switch to a heat pump waterheater.

FIG. 26 is a block diagram depicting, by way of example, the annualenergy consumption of FIG. 22 reflecting a switch to a heat pump spaceheater.

FIG. 27 is a block diagram depicting, by way of example, the annualenergy consumption of FIG. 22 with cumulative revised energy consumptionexpressed in kilowatt hours.

FIG. 28 is a block diagram depicting, by way of example, the cumulativerevised energy consumption of FIG. 27 overlaying a 20% efficientphotovoltaic power generation system.

FIG. 29 is a block diagram showing a computer-implemented system 140 forempirically estimating overall thermal performance of a building througha short-duration controlled test, in accordance with one embodiment.

DETAILED DESCRIPTION

Private individuals enjoy an immediacy to decision-making on matters ofenergy consumption and supply. As a result, individuals are ideallypositioned to make the kinds of changes necessary to decrease theirpersonal energy consumption and avoid energy waste, and to chooseappropriate sources of renewable energy, among other actions. However,merely having a motivation to better balance energy consumption andsupply, including adopting a ZNE goal, is not enough, as the possibleways that personal energy consumption can be improved are myriad, andnavigating through the option space can be time-consuming andfrustrating. Individual consumers need, but often lack, the informationnecessary to guide the energy consumption and supply decisions that arerequired to accomplish their conservational goals, particularly when aswitch to an alternative on-site energy source has already been madewithout first determining how efficiently energy is being consumed in abuilding.

The problem of providing consumers with the kinds of information neededto wisely make energy-related decisions can be approached by firstdeveloping a cost model that depicts the energy consumption landscape ofthe average consumer. FIG. 1 is a Venn diagram showing, by way ofexample, a typical consumer's energy-related costs 10. The costs 10include both fuel costs and operational costs, where appropriate, whichprovide the basis of the cost model. For purposes of illustration, thecost model assumes that the hypothetical consumer has a privateresidence, as opposed to an apartment or condominium, and uses apersonal vehicle as a primary mode of transportation, rather than publicmass transit or a physical mode of travel. The cost model can be adaptedmutatis mutandis to other modeling scenarios for apartment dwellers orurban city commuters, for instance, who may have other energyconsumption and supply types of expenses.

The cost model reflects the choices made by consumers that affect theirenergy consumption. For example, residential consumers must choosebetween various energy options or alternatives concerning weatherstripping or caulking to seal a house; increased ceiling, floor, andwall insulation; high-efficiency windows; window treatments;programmable thermostats; cool roofs, that is, roofs that have a highsolar reflectance; radiant barriers; roof venting; electric and naturalgas furnaces for space heating; air source and geothermal heat pumps forspace heating and cooling; compressive and evaporative air conditioners;natural gas or electric and tank-based or tank-less water heaters; airsource heat pump water heaters; incandescent, fluorescent, and LEDlights; high efficiency appliances, including clothes washers, clothesdryers, refrigerators, dishwashers, and microwave ovens; electric(conductive and inductive) and natural gas stoves; electric and naturalgas ovens; and electronic equipment that consume electricity, such asWi-Fi routers, televisions, stereos, and so on. Consumers must alsochoose between standard gasoline- or diesel-fueled vehicles; hybridgasoline- or diesel-fueled vehicles; natural gas vehicles; plug-inhybrid electric vehicles; and pure electric vehicles.

The cost model also reflects the choices made by consumers that affecttheir energy supply. A consumer can be faced purchasing energy, that is,electricity and natural gas, from their local utility; purchasinggasoline, diesel or other automobile fuel from a gasoline station;generating hot water using solar hot water heating; and generatingelectricity, either for home or transportation purposes, usingphotovoltaic power generation systems or, less commonly, small wind,small hydroelectric, or other distributed power generation technologies.

In the cost model, the energy-related costs 10 can be divided into twocategories, home energy costs 11 and personal transportation costs 12.Home energy costs 11 may include energy consumed for space heating andcooling 13, lighting 14, cooking 15, powering appliances and electricaldevices 16, heating water 17, and doing laundry 18, although fewer ormore home energy costs may also be possible, such as where a consumerlacks in-home laundry facilities. Personal transportation costs 12 mayinclude the actual cost of the vehicle 19, fuel costs 20, andmaintenance expenses 21, although fewer or more transportation costs mayalso be possible, such as where a company car is provided to theconsumer free of charge.

Home energy costs 11 can be sub-grouped into those costs that are alwaysin the form of electricity consumption 22. These costs include lighting14 and (most) appliances and electrical devices 16. For these types ofcosts, the only practicable options to lower energy consumption arereplacing lighting fixtures, appliances, or electrical devices withhigher efficiency units or modifying or eliminating their usage. Theremaining home energy costs 11 could either be due to electricityconsumption or consumption of energy from other sources, depending uponthe type of fixtures or appliances used. A gas range, for instance,consumes a minimal amount of electricity, as heat for cooking and bakingare generated from natural gas, whereas an electric range can consume asignificant amount of electricity, when used heavily. This dichotomy ofelectricity-dependent energy costs and energy costs that could be basedon some other form of energy further complicates the energy consumptionlandscape of the average consumer.

Power utilities and energy agencies often promote energy conservation byproviding periodic net energy consumption statistics to their customers.Such statistics are helpful in determining fuel costs for electricityand emphasize energy costs that are always in the form of electricityconsumption 22. On the other hand, these statistics can hide underlyinginefficiencies in overall energy consumption, particularly where aconsumer has already made a switch to an alternative energy source, byonly showing a partial picture of gross energy consumption, as furtherdescribed infra beginning with FIG. et seq.

For purposes of the cost model, fuel costs include electricity (E); fuelfor heating (F), which could be natural gas, propane, or fuel oil; andfuel for transportation (G), which could be gasoline, diesel, propane,LPG, or other automobile fuel. In addition, maintenance costs will beincluded in the cost model. A consumer's total energy-related Costs(C^(Total)) equals the sum of the electricity cost (C^(E)), fuel forheating cost (C^(F)), gasoline (or other automobile fuel) cost (C^(G)),and maintenance cost (C^(M)), which can be expressed as:

C ^(Total) =C ^(E) +C ^(F) +C ^(G) +C ^(M)  (1)

In Equation (1), each cost component can be represented as the productof average price and annual quantity consumed, assuming that the priceis zero when the quantity consumed is zero. As a result, the totalenergy-related costs C^(Total) can be expressed as:

C _(Total) =P ^(E) Q ^(E) +P ^(F) Q ^(F) +P ^(G) Q ^(G) +P ^(M) Q^(M)  (2)

Price and quantity in Equation (2) need to be consistent with eachother, but price and quantity do not need to be the same across all costcomponents. Fuel units depend upon the type of fuel. Electricity price(P^(E)) is expressed in dollars per kilowatt hour ($/kWh) andelectricity quantity (Q^(E)) is expressed in kilowatt hours (kWh). Fornatural gas, fuel for heating price (P^(F)) is expressed in dollars perthermal unit ($/therm) and fuel quantity (Q^(F)) is expressed in thermalunits (therms). Gasoline (or other automobile fuel) price (P^(G)) isexpressed in dollars per gallon ($/gallon) and gasoline quantity (Q^(G))is expressed in gallons. If only automobile maintenance costs areincluded and not the vehicle cost, maintenance price (P^(M)) can be indollars per mile driven ($/mile) and maintenance quantity (Q^(M)) can beexpressed in miles.

Pricing of fuel for heating (P^(F)) may be a function of the amount offuel consumed or could be a non-linear value, that is, a valuedetermined independent of amount used, or a combination of amount andseparate charges. In the cost model, for clarity, the fuel for heatingcost (C^(F)) assumes that the quantity of fuel actually used for spaceheating is separable from other loads in a home that consume the sametype of fuel, as further explained infra.

For fuels for heating sold by bulk quantity, such as propane or fueloil, fuel pricing is typically on a per-unit quantity basis. For otherfuels for heating, such as natural gas, a number of utilities havetiered natural pricing that depend upon the quantity consumed. Inparticular, electricity pricing can be complicated and may depend upon avariety of factors, including the amount of electricity purchased over aset time period, such as monthly, for instance, tiered electricityprices; the timing of the electricity purchases, for instance,time-of-use electricity prices; fixed system charges; and so forth. As aresult, accurately calculating average electricity pricing oftenrequires detailed time series electricity consumption data combined withelectricity rate structures. Conventional programs and online servicesare available to perform electricity pricing calculations. A slightlydifferent formulation of electricity pricing may be used where thequantity of electricity purchased nets out to zero consumption, but thetotal cost does not, such as can occur due to a flat service surcharge.

In the cost model, the quantity of electricity (Q^(E)), fuel for heating(Q^(F)), and gasoline (or other automobile fuel) (Q^(G)) purchased isassumed to equal the quantity consumed for meeting the consumer's energyconsumption requirements. Gasoline (or other automobile fuel) fuelquantity (Q^(G)) can be fairly estimated based on miles driven annuallyover observed or stated vehicle fuel efficiency, such as available fromhttp://www.fueleconomy.gov Electricity quantity (Q^(E)) can generally beobtained from power utility bills

The quantity of fuel for heating (Q^(F)) grossly represents the amountof fuel that needs to be purchased to provide the desired amount of heatin the consumer's home. The amount of fuel used for heating may actuallybe smaller than the total amount of fuel delivered to the home;depending upon the types of components installed in a home, the fuelused for heating may also be the same fuel used for other purposes,which may include fuel used, for example, for heating water, cooking, ordrying clothes. Notwithstanding, utilities that provide fuel to theircustomers for heating and other purposes, in particular, natural gas,via piped-in public utility service generally meter net fuel purchasesat the point of delivery. Individual loads are not metered. Thus, thetotal quantity of fuel (Q^(F)) consumed may need to be divided into theamount of fuel used strictly for space heating (Q^(F-Heating)) and theamount of fuel used for other non-space heating purposes(Q^(F-Non-Heating)). For instance, in many residential situations, muchof) the non-space heating fuel will be used for water heating. Theload-corrected quantity of fuel (Q^(F)) can be expressed as:

Q ^(F) =Q ^(F-Heating) +Q ^(F-Non-Heating)  (3)

Modeling the quantity of fuel consumed for space heating (Q^(F))requires consideration of the type of space heating employed in a home.A separate quantity of fuel for space heating is only required if thetype of heating system used does not use electricity for active heatgeneration. Active heating sources, such as central heating systems,include a heating element that heats the air or water, for instance, afurnace or boiler, and a heating delivery or distribution component,such as ductwork through which the heated air is forced by an electricfan or pipes through which the heated water is circulated via anelectric pump. Thus, where the heating element requires, for instance,natural gas, propane, or fuel oil to generate heat, the quantity of fuelfor space heating consumed will be equal to the consumer's energyconsumption for space heating requirements. In contrast, where theheating element relies on electricity for active heat generation, suchas passive radiant heating or an electric-powered air source heat pump,the quantity of fuel for space heating will be zero, although the totalquantity of electricity (Q^(E)) consumed will be significantly higherdue to the electricity used for heat generation. The fuel for spaceheating quantity (Q^(F)) can be normalized to the quantity ofelectricity (Q^(E)) for purposes of comparison. Estimating the amount offuel consumed for space heating requirements will now be discussed.

The overall rate of heat transfer of a building equals the rate of theheat transfer or conduction through each unique building surface plusthe rate of heat transfer through infiltration, that is, air leakageinto a building. Conduction rate and infiltration rate are based on thethermal characteristics of the material in each surface of the buildingand upon the indoor and outdoor temperatures and airtightness of thebuilding.

Heat transfer can be individually calculated for each building surface,then summed to yield overall heat transfer. Alternatively, a building'soverall thermal performance (UA^(Total)) can first be calculated,expressed in units of Btu per ° F.-hour. Overall thermal performance canthen be combined with the difference between the indoor and outdoortemperature. When the latter approach is used, the heat loss over aone-hour period Q^(Heat Loss) equals UA^(Total) times the differencebetween the average indoor and outdoor temperature times one hour, whichcan be expressed as:

Q ^(Heat Loss)=(UA ^(Total))(T _(Indoor) −T _(Outdoor))(1 hour)  (4)

Equation (4) can be rearranged to yield UA^(Total):

$\begin{matrix}{{UA^{Total}} = \frac{Q^{{Heat}{Loss}}}{( {T_{Indoo\tau} - T_{Outdoor}} )( {1hour} )}} & (5)\end{matrix}$

Total heat loss Q^(Heat Loss) can be analytically estimated based onfurnace sizing for the building, such as described in H. Rutkowski,Manual J Residential Load Calculation, (8^(th) ed. 2011) (“Manual J”),and also as provided via the Air Conditioning Contractors of America'sWeb-fillable Form RPER 1.01, available at http://www.acca.org. Per theManual J approach, winter and summer design conditions are specified,including indoor and outdoor temperatures. In addition, surfacemeasurements and materials, estimated infiltration, heating and coolingequipment capacities, and duct distribution system design are specified

These values are used in the Manual J approach to estimate total heatloss per hour, from which a recommended heating output capacity isdetermined. For example, a heating system having a 64,000 Btu/hourheating output capacity would be appropriate in a building with anestimated total heat loss of 59,326 Btu/hour. Assuming an outdoortemperature of −6° F. and an indoor temperature of 70° F., Equation (5)can be used to estimate UA^(Total) based on the estimated total heatloss of 59,326 Btu/hour, such that:

$\begin{matrix}{{UA^{Total}} = {\frac{59,326{Btu}}{\lbrack {70{^\circ}{F.{- ( {{- 6}{^\circ}{F.}} )}}} \rbrack( {1{hour}} )} = \frac{781{Btu}}{{^\circ}{F.{- {hour}}}}}} & (6)\end{matrix}$

The result is that this building's overall thermal performance is 781Btu/hr-° F. Other ways of estimating total heat loss Q^(Heat Loss) arepossible.

Equation (4) provides an estimate of the heat loss over a one-hourperiod Q^(Heat Loss) for a building. Equation (4) can also be used toderive the amount of heat that needs to be delivered to a buildingQ^(Heat Delivered) by multiplying the building's overall thermalperformance UA^(Total), times 24 hours per day, times the number ofHeating Degree Days, such as described in J. Randolf et al., Energy forSustainability: Technology, Planning, Policy, p. 248 (2008), which canbe expressed as:

Q ^(Heat Delivered)=(UA ^(Total))(24)(HDD_(Location) ^(Set Point Temp))

The number of Heating Degree Days, expressed as HDD_(Location)^(Set Point Temp) in ° F.-day per year, is determined by the desiredindoor temperature and geographic location and can be provided by lookuptables.

In turn, the annual amount of heat delivered by a furnace to a buildingfor end-use Q^(Heat Delivered-Furnace), expressed in Btu per hour,equals the product of furnace fuel requirements R^(Furnace), alsoexpressed in Btu per hour, percentage of furnace efficiency η^(Furnace),percentage of delivery system efficiency η^(Delivery), and hours ofoperation Running-Time, such that:

Q ^(Heat Delivered-Furnace)=(R^(Furnace))(η^(Furnace)η^(Delivery))(Running-Time)  (8)

The annual amount of heat delivered Q^(Heat Delivered-Furnace) can bediscounted by the amount of energy passively obtained on-site. Forinstance, if the solar savings fraction (SSF) represents the fraction ofenergy by a building due to solar gains, the heat that needs to bedelivered by the furnace can be expressed by:

Q ^(Heat Delivered-Furnace) =Q ^(Heat Delivered)(1−SFF)  (9)

For the time being, ignore any gains in indoor temperature due tointernal sources of heat.

The amount of fuel used strictly for space heating Q^(F-Heating) can befound by substituting Equation (7) into Equation (9), setting the resultequal to Equation (8), and solving for Q^(F-Heating). The amount of fuelthat needs to be purchased for space heating uses Q^(F-Heating) equalsthe product of furnace fuel requirements R^(Furnace) and hours ofoperation hours Running-Time. Thus, solving for Q^(F-Heating):

$\begin{matrix}{Q^{F - {Heating}} = \frac{( {UA^{Total}} )( {24} )( {HDD_{Location}^{{Set}{Point}{Temp}}} )( {1 - {SSF}} )}{\eta^{Furnace}\eta^{D{elivery}}}} & (10)\end{matrix}$

Calculating the solar savings fraction SSF typically requires extensivecomputer modeling. However, for an existing building, the SSF can bedetermined by setting Equation (10) equal to the amount of fuel requiredfor space heating and solving for the solar savings fraction.

In general, utilities that provide fuel to their customers via piped-inpublic utility services meter fuel purchases at the point of deliveryand not by individual component load. In situations where the fuel isused for purposes other than solely space heating, the total fuelpurchased for space heating Q^(F-Heating) may only represent a fractionof the total fuel purchased Q^(F). Q^(F-Heating) can be expressed as:

Q ^(F-Heating)=(H)(Q ^(F))  (11)

where H fractionally represents the percentage of the total fuelpurchased for space heating purposes.

The fraction H can be empirically inferred from fuel purchase data. Fuelpurchased in the months occurring outside of the heating season areassumed to represent the fuel purchased for non-space heating needs andcan be considered to represent a constant baseline fuel expense. FIG. 2is a flow diagram showing a function 30 for fractionally inferring thepercentage of the total fuel purchased for space heating purposes, inaccordance with one embodiment. The function 30 can be implemented insoftware and execution of the software can be performed on a computersystem, such as further described infra with reference to FIG. 29 , as aseries of process or method modules or steps.

Initially, fuel purchase data is obtained (step 31), such as can beprovided by the fuel utility. Preferably, the data reflects fuelpurchases made on at least a monthly basis from the utility. An averageof the fuel purchased monthly during non-heating season months iscalculated (step 32). In some regions, the heating season will onlyinclude traditional winter months, beginning around mid-December andending around mid-March; however, in most other regions, space heatingmay be required increasingly in the months preceding winter anddecreasingly in the months following winter, which will result in anextended heating season.

Each month (or time increment represented by each fuel purchase) is theniteratively processed (steps 33-40), as follows. For each month (step33), the fuel purchase for that month is chosen (step 34) and added to arunning total of annual fuel purchases (step 35). If the monthly fuelpurchase is greater than the average of the fuel purchased monthlyduring non-heating season months (step 36), the average of the fuelpurchased monthly is subtracted from that monthly fuel purchase (step37) and the remainder represents the fuel purchased for space heating inthat month. Otherwise, the monthly fuel purchase is subtracted fromitself (step 38), effectively indicating that the fuel purchased forspace heating in that month is zero. The difference of the subtraction,that is, the fuel purchased for space heating in that month, is added toa running total of annual space heating fuel purchases (step 39), andthe process repeats for each subsequent month (step 40). Finally, theratio of the running total of annual space heating fuel purchases to therunning total of annual fuel purchases is returned (step 41) as thefraction H.

The relationship between total annual fuel purchases and total annualspace heating fuel purchases can be visualized. FIG. 3 is a graph 50depicting, by way of example, annual fuel purchases, including fuelpurchased for space heating purposes. The x-axis 51 represents months.The y-axis 52 represents natural gas consumption, expressed in thermsper day. May through September are considered non-winter (non-heatingseason) months. The natural gas (fuel) purchases 53 for each month aredepicted as circles. Total annual fuel purchases 54 can be interpolatedby connecting each monthly natural gas purchase 53. The fraction H forthe percentage of the total fuel purchased for space heating purposeseach month is determined, from which a baseline annual fuel expense 55can be drawn. The region between the baseline annual fuel expense 55 andthe interpolated total annual fuel purchases 54 represents the totalannual space heating (fuel) purchases 56.

The relationship between the total annual fuel purchases, baseline fuelexpenses, and total space heating purchases can be formalized. First,the average monthly fuel purchased for non-winter monthsQ^(F-Non-Winter) over a set number of months is calculated, as follows:

$\begin{matrix}{\overset{\_}{Q^{{F - {Non}} - {Winter}}} = \frac{\Sigma_{i = {{Non} - {Winter}{Start}{Month}}}^{{Non} - {Winter}{End}{Month}}{Fuel}{}{Purchased}_{i}}{{Number}{of}{Months}}} & (12)\end{matrix}$

where i represents the range of non-winter months within the set numberof months; and Fuel Purchased₁ represents the fuel purchased in thenon-winter month i.

Next, the fuel consumed each month for heating, which is the differencebetween the monthly fuel purchase and the minimum of either the monthlyfuel purchase or the average monthly fuel purchased for non-wintermonths, is added to a summation to yield the total annual fuel consumedfor heating Q^(F-Heating) as follows:

$\begin{matrix}{Q^{F - {Heating}} = {\sum\limits_{i = 1}^{12}( {{{Fuel}{Purchased}_{i}} - {\min( {{{Fuel}{Purchased}_{i}},\overset{\_}{Q^{{F - {Non}} - {Winter}}}} )}} )}} & (13)\end{matrix}$

Assuming that the total annual fuel purchases Q^(F) are non-zero, theratio of the total annual fuel consumed for heating Q^(F-Heating) andthe total fuel purchases Q^(F) is taken to yield the fraction H, asfollows:

$\begin{matrix}{H = \frac{Q^{F - {Heating}}}{Q^{F}}} & (14)\end{matrix}$

Finally, the percent of heat supplied by the solar savings fraction canbe determined by setting Equation (10) equal to Equation (11) andsolving for SSF, in accordance with:

$\begin{matrix}{{SSF} = {1 - \frac{(H)( Q^{F} )( \eta^{Furnace} )( \eta^{D{elivery}} )}{( {UA^{Total}} )( {24} )( {HDD_{Location}^{{Set}{Point}{Temp}}} )}}} & (15)\end{matrix}$

A building's overall thermal performance UA^(Total) is key to estimatingthe amount of fuel consumed for space heating requirements. Equation(5), discussed supra, presents one approach to estimating UA^(Total),provided that the total heat loss Q^(Heat Loss) can be estimated. Ananalytical approach to determining UA^(Total) requires a detailed energyaudit, from which UA^(Total) is then calculated using a set ofindustry-standard engineering equations. With both approaches, thebuilding's actual thermal performance is not directly measured. A thirdapproach through UA^(Total) can be empirically quantified will now bepresented.

The total heat transfer of a building at any instant in time (q^(Total))equals the sum of the heat transferred through the building envelope byconduction (q^(Envelope)) plus the heat transferred through infiltration(q^(Infiltration)) which can be expressed as:

q ^(Total) =q ^(envelope) +q ^(Infiltration)  (16)

An energy audit does not directly measure the heat transferred throughthe building envelope by conduction q^(Envelope). Rather, q^(Envelope)is calculated using a series of steps. First, the surface areas of allnon-homogeneous exterior-facing surfaces are either physically measuredor verified, such as by consulting plans for the building.Non-homogeneous surfaces are those areas that have different insulatingmaterials or thicknesses. The surface areas of all floors, walls,ceilings, and windows are included.

Second, the insulating properties of the materials used, quantified as“R-values,” or the capacity of an insulating material to resist heatflow for all surfaces area determined. R-values are generally determinedby visual inspection, if the insulation is exposed, such as insulationbatts used in an attic. When the insulation cannot be visuallyinspected, as with wall insulation, R-values are estimated based onsurface thickness and the age of the building

These first two steps are difficult, time-consuming, and carry the riskof mistakes. Accurately measuring all of the exterior-facing surfacescan be tedious, and the manual nature of the visual inspection admits oferror. For instance, some wall surfaces may appear to be onlyinterior-facing, yet parts of a wall may actually be both interior- andexterior-facing, as can happen in a split-level home along the walldividing the “split” sections of the house (also referred to as a kneewall). When viewed from inside, the wall along the split, on both sides,appears to be an interior-facing wall, yet the upper section of thatwall is often partially exposed to the exterior along the outer wallsurface extending beyond the ceiling height of the lower section of thesplit. In addition, issues, such as improperly installed insulation andinsulation falling away from a wall, can be missed by a visualinspection

Third, the R-values are inverted to yield U-values, which are thenmultiplied by their corresponding surface areas. The results are summedacross all N surfaces of the building. Total heat transfer through thebuilding envelope by conduction q^(Envelope) equals the product of thissummation times the difference between the indoor and outdoortemperatures, expressed as:

$\begin{matrix}{q^{Envelope} = {( {\sum\limits_{i = 1}^{N}{U^{i}A^{i}}} )( {T^{Indoor} - T^{Outdoor}} )}} & (17)\end{matrix}$

where U^(i) represents the U-value of surface i: A^(i) represents thesurface area of surface i; and T^(Indoor) and T^(Outdoor) arerespectively the indoor and outdoor temperatures relative to thebuilding.

Heat transfer also occurs due to infiltration. “A major load for yourfurnace is heating up cold air leaking into your house, while warmindoor air leaks out. These infiltration losses are driven in part bythe difference in the indoor-to-outdoor temperature (stack-driveninfiltration) and in part by the pressure differences caused by the windblowing against the side of the house (wind-driven insolation).” J.Randolf et al. at p. 238, cited supra. Formally, the rate of heattransfer due to infiltration q^(Infiltration) can be expressed as:

q ^(Infiltration) =ρcnV((T ^(Indoor) −T ^(Outdoor))  (18)

where ρ represents the density of air, expressed in pounds per cubicfoot; c represents the specific heat of air, expressed in Btu per pound° F.; n is the number of air changes per hour, expressed in number perhour; and V represents the volume of air per air change, expressed incubic feet per air change.

In Equation (18), ρ and care constants and are the same for allbuildings; ρ equals 0.075 lbs/ft³ and c equals 0.24 Btu/lb-° F. n andTare building-specific values. V can be measured directly or can beapproximated by multiplying building square footage times the averageroom height. Measuring n, the number of air changes per hour, requiressignificant effort and can be directly measured using a blower doortest.

Total heat transfer q^(Total) can now be determined. To review,q^(Total) equals the sum of the heat transfer through the buildingenvelope by conduction q^(Envelope) plus the heat transfer throughinfiltration q^(Infiltration). Substitute Equation (17) and Equation(18) into Equation (16) to express the rate of heat loss q^(Total) forboth components:

q ^(Total) =UA ^(Total)(T ^(Indoor) −T ^(Outdoor))  (19)

where:

$\begin{matrix}{{UA^{Total}} = {( {\sum\limits_{i = 1}^{N}{U^{i}A^{i}}} ) + {\rho cnV}}} & (20)\end{matrix}$

Equation (19) presents the rate of heat transfer q^(Total) at a giveninstant in time.

Instantaneous heat transfer can be converted to total heat transfer overtime Q_(Δt) ^(Total) by adding a time subscript to the temperaturevariables and integrating over time. UA^(Total) is constant over time.Integrating Equation (19), with UA^(Total) factored out, results in:

Q _(Δt) ^(Total) =UA ^(Total)∫_(t) ₀ ^(t) ⁰ ^(+Δt)(T _(t) ^(Indoor) −T_(t) ^(Outdoor))dt  (21)

Equation (21) can be used in several ways. One common application of theequation is to calculate annual fuel requirements for space heating.Building occupants typically desire to maintain a fixed indoortemperature during the summer and a different fixed indoor temperatureduring the winter. By the same token, building operators typically wantto determine the costs of maintaining these desired indoor temperatures

For example, take the case of maintaining a fixed indoor temperatureduring the winter. Let the temperature be represented byT^(Indoor-Set Point Temp) and let Δt equal one year. Equation (21) canbe modified to calculate the annual heat loss Q_(Annual) ^(Heat Loss) byadding a maximum term, such that:

Q _(Annual) ^(Heat Loss) =UA ^(Total)∫_(t) ₀ ^(t) ⁰ ^(+Δt)max(T _(t)^(Indoor-Set Point Temp) −T _(t) ^(Outdoor),0)dt  (22)

Solving Equation (22) yields:

Q _(Annual) ^(Heat Loss) =UA^(Total)(24*HDD^(Indoor-Set Point Temp))  (23)

where HDD represents the number of degree days when the outdoortemperature exceeds the desired indoor temperature. A typical indoortemperature used to calculate HDD is 65° F.

Equation (23) is a widely-used equation to calculate annual heat loss.UA^(Total) is the core, building-specific parameter required to performthe calculation. UA^(Total) represents the building's overall thermalperformance, including heat loss through both the building envelopethrough conduction and heat loss through infiltration. Conventionalpractice requires an energy audit to determine UA^(Total), whichrequires recording physical dimension, visually inspecting or inferringR-values, and performing a blower door test. A formal energy audit canrequire many hours and can be quite expensive to perform. However,UA^(Total) can be empirically derived.

In slightly modified form, Equation (21) can be used to calculateHeating (or Cooling) Degree Days for estimating fuel costs for aone-year period by assuming that the indoor temperature is constant. Theequation can also be used to calculate short-term heat loss, as part ofan input to an empirical approach to deriving a building's overallthermal performance UA^(Total). FIG. 4 is a flow diagram showing methodfor empirically estimating overall thermal performance of a building 60through a short-duration controlled test, in accordance with oneembodiment. The method 60 requires the use of a controllable heating (orcooling) source, and the measurement and analysis aspects of the method60 can be implemented in software. Execution of the software can beperformed with the assistance a computer system, such as furtherdescribed infra with reference to FIG. 29 , as a series of process ormethod modules or steps.

Briefly, the empirical approach is to perform a controlled test over ashort duration, for instance, 12 hours. During the controlled test, heatloss from a building occurs and a controllable heat source, such as afurnace, is subsequently used to compensate for the heat loss.Preferably, the controlled test is performed during the winter months.The same controlled test approach can be used during the summer months,where heat gain occurs and a controllable cooling source, such as an airconditioner, is subsequently used to compensate for the heat gain.

As a preliminary step, an appropriate testing period is chosen, duringwhich heat gain is controllable, such as during the night, when solargain will not be experienced. FIG. 5 is a graph depicting, by way ofexample, the controlled, short-duration test of FIG. 4 . The x-axis 81represents time of day. The y-axis 82 represents temperature in ° F. Thetesting period is divided into an unheated period that occurs from timet₀ to time t₁, a heated period that occurs from time t₁ to time t₂, anda stabilizing period that occurs from time t₂ to time t₃. At a minimum,indoor temperature 83 is measured at times t₀, t₁, and t₃, althoughadditional indoor temperature measurements will increase the accuracy ofthe controlled test. Outdoor temperature 84 may optionally be measuredat times t₀ and t₃ and additional outdoor temperature measurements willalso increase the controlled test's accuracy. Additionally, an expectedfinal indoor temperature 85 is estimated based on a projection of whatthe indoor temperature would have been at time t₃, had the heatingsource not been turned back on at time t₁.

The starting time t₀ of the unheated period should start when the indoortemperature has stabilized due to the effects of thermal mass. Theunheated period is of a duration sufficient to allow for measurable heatloss, such as a period of around 12 hours, although other periods oftime are possible. The heating source is run for a short duration duringthe heated period, such as for an hour or so, preferably early in themorning before the sun rises. The stabilizing period provides a time lagfor a short duration, such as an hour or so, to allow the indoortemperature to stabilize due to the effects of thermal mass. Otherfactors can be included in the controlled test, such as heat gain fromoccupants or other heat sources inside the building

Referring back to FIG. 4 , a baseline indoor temperature T₀ is recordedat the outset of an unheated period at time t₀ (step 61), at which timeoperation of the heating source is also stopped (step 62). The methodpauses during the unheated period from time t₀ to time t₁ (step 63). Astarting indoor temperature T₁ is recorded at the outset of a heatedperiod at time t₁ (step 64), at which time operation of the heatingsource is also temporarily resumed (step 65). The method pauses duringthe heated period from time t₁ to time t₂ (step 66). Operation of theheating source is again stopped at the end of the heated period at timet₂ (step 67). The method pauses during a stabilizing period from time t₂to time t₃ (step 68). A final indoor temperature T₃ is recorded at theend of a stabilizing period at time t₃ (step 69)

Next, the amount of energy consumed over testing period from time t₀ totime t₃ is measured (step 70). The energy is assumed to equal the totalamount of heat gained inside the building from internal sources of heat(Q^(Internal)); inclusion of independent sources of heat gain, such asfrom occupants, will increase accuracy. Finally, the overall thermalperformance of the building UA^(Total) and distribution efficiency areestimated (step 71), as follows.

First, the heat loss over the unheated period from time t₀ to time t₁ iscalculated, that is, by setting Δt to around 12 hours. Solving Equation(21) yields:

Q _(Δt) ^(Total) −UA ^(Total)( T _(Δt) ^(Indoor) − T _(Δt) ^(Outdoor))Δt

where T_(Δt) ^(Indoor) is the average indoor temperature and T_(Δt)^(Outdoor) is the average outdoor temperature.

Next, the heat gain by operating the heating source over the heatedperiod from time t₁ to time t₂ is calculated using Equation (8). Theamount of energy required to return the building to the baseline indoortemperature T₀ can be approximated by dividing the delivered heat by thepercent of heat loss that was restored using the controlled heat source.The amount of heat restored is assumed to be proportional to threetemperatures, the baseline indoor temperature T₀, the final indoortemperature T₃, and an expected final indoor temperature T₃ ^(No Heat),which is an estimated temperature based on a projection of what theindoor temperature would have been at time t₃, had the heating sourcenot been turned back on at time t₁. Assuming that T₀≠T₃ ^(No Heat), thepercentage of energy lost provided by the heat source equals:

$\begin{matrix}{{{Percent}{Restored}} = \frac{T_{3} - T_{3}^{{No}{Heat}}}{T_{0} - T_{3}^{{No}{Heat}}}} & (25)\end{matrix}$

The hours of operation of the heating source equal t₂ minus t₁. Thus,the heat gain required to replace the lost heat equals Equation (8)divided by Equation (25), expressed as:

$\begin{matrix}{Q^{{Heat}{Delivered} - {Furnace}} = {( R^{Furnace} )( {\eta^{Furnace}\eta^{Delivery}} )( {t_{2} - t_{1}} )( \frac{T_{0} - T_{3}^{{No}{Heat}}}{T_{3} - T_{3}^{{No}{Heat}}} )}} & (26)\end{matrix}$

In addition, heat was gained inside the building from internal sourcesof heat. Set Equation (33) plus heat delivered through internal gainsQ^(Internal) equal to Equation (24) and solve for overall thermalperformance UA^(Total):

${UA}^{Total} = \begin{matrix}\frac{\lbrack \frac{( R^{Furnace} )( \eta^{Furnace} )( \eta^{Delivery} )( {t_{2} - t_{1}} )( {T_{0} - T_{3}^{{No}{Heater}}} )}{( {T_{3} - T_{3}^{{No}{Heater}}} )} \rbrack + Q^{Internal}}{( {\overset{\_}{T_{\Delta t}^{Indoor}} - \overset{\_}{T_{\Delta t}^{Ambient}}} )( {t_{3} - t_{0}} )} & (27)\end{matrix}$

The controlled test approach has been empirically validated. The testingprocedure was conducted at approximately the same time of day on twoseparate days with different weather conditions for a house in Napa,Calif. The first test was started on Jan. 12, 2014 and the second testwas started on Jan. 13, 2014. There was a difference of about 15° F. inoutdoor temperature at the start of the testing on the two days. Inaddition, the heating source was only operated for the amount of timenecessary to return the house to the baseline temperature for the firsttest, while the heating source was not operated for a sufficiently longtime to return the house to the baseline temperature for the secondtest. The recorded indoor and outdoor temperatures for the testconducted on Jan. 12, 2014 is shown in FIG. 5 . Similarly, FIG. 6 is agraph depicting, by way of example, the controlled, short-duration testof FIG. 4 for Jan. 13, 2014. As before, the x-axis represents time ofday and the y-axis represents temperature in ° F. Assuming an 80%delivery efficiency η^(Delivery), results indicate that the house'soverall thermal performance UA^(Total) was 525 for the first test and470 for the second test. These results are within approximately 10percent of each other. In addition, an independent Certified Home EnergyRating System (HERS) rater was hired to perform an independent energyaudit of the house. The results of the HERS audit compared favorably tothe results of the empirical approach described supra with reference toFIG. 4 .

The methods described herein can be used to equip consumers with thekinds of information necessary to make intelligent energy decisions. Anexample of how to apply the results to a particular situation will nowbe presented.

Example: A residential homeowner has an old heating, ventilation, andair conditioning (HVAC) system that is on the verge of failure. Theconsumer is evaluating two options:

Option 1: Replace the existing HVAC system with a system that has thesame efficiency and make no other building envelope investments in thehouse, at the cost of $9,000.

Option 2: Take advantage of a whole house rebate program that theconsumer's utility is offering and simultaneously upgrade multiplesystems in the house. The upgrades include increasing ceilinginsulation, replacing ductwork, converting the natural gas-powered spaceheating furnace and electric air conditioner to electric-powered airsource heat pumps, and providing enough annual energy to power the heatpump using a photovoltaic system

In this example, the following assumptions apply:

-   -   The consumer's annual natural gas bill is $600, 60 percent of        which is for space heating. The natural gas price is $1 per        therm.    -   The existing furnace has an efficiency of 80 percent and the        existing ductwork has an efficiency of 78 percent.    -   Adding four inches of insulation to the 1,100 ft² ceiling, to        increase the R-Value from 13 to 26, will cost $300.    -   Photovoltaic power production costs $4,000 per kW_(DC), produces        1,400 kWh/kW_(DC)-yr, and qualifies for a 30-percent federal tax        credit.    -   The heat pump proposed in Option 2 has a Heating Season        Performance Factor (HSPF) of 9 Btu/Wh and a Seasonal Energy        Efficiency Ratio (SEER) identical to the existing air        conditioner. The heat pump will cost $10,000.    -   The ductwork proposed in Option 2 will be 97 percent efficient        and will cost $3,000.    -   The consumer will receive a $4,000 rebate from the utility for        the whole house upgrade under Option 2.

Analysis of the options requires determining the overall thermalcharacteristics of the existing building, evaluating the effects ofswitching fuel sources, comparing furnace efficiency, and determiningfuel requirements. For purposes of illustration, the calculation in theexample will only include the heating characteristics

In this example, the consumer performed the empirical approach describedsupra with reference to FIG. 4 to empirically estimate overall thermalperformance of a building and determined that the UA^(Total) for hishouse was 450. Option 2 presents multiple changes that need to beconsidered. First, Option 2 would require switching fuels from naturalgas to electricity. Assume conversion factors of 99,976 Btu per thermand 3,412 Btu per kWh. Converting current energy usage, as expressed intherms, to an equivalent number of kWh yields:

$\begin{matrix}{Q^{F} = {{( {600{thems}} )( \frac{99,976{Btu}}{therm} )( \frac{1{kWh}}{3,412{Btu}} )} = {17,581{kWh}}}} & (28)\end{matrix}$

Second, the heat pump is 264 percent efficient at converting electricityto heat. The equivalent furnace efficiency {circumflex over(η)}^(Furnace) of the heat pump is:

$\begin{matrix}{{\hat{\eta}}^{Furnace} = {{( \frac{9{Btu}}{Wh} )( \frac{1,000{Wh}}{kWh} )( \frac{1{kWh}}{3,412{Btu}} )} = {264\%}}} & (29)\end{matrix}$

Third, the annual amount of electricity required to power the heat pumpcan be determined with Equation (42), as further described infra, withthe superscript changed from ‘F’ (for natural gas fuel) to ‘E’ (forelectricity):

$\begin{matrix}\begin{matrix}{{\hat{Q}}^{E - {Heating}} = {(0.6){( {17,581} )\lbrack {1 - \frac{( {\frac{1}{13} - \frac{1}{26}} )( {1,100} )}{450}} \rbrack}( \frac{0.8}{2.64} )( \frac{0.78}{0.97} )}} \\{= {2,351{kWh}}}\end{matrix} & (30)\end{matrix}$

Fourth, in addition to switching from natural gas to electricity, theconsumer will be switching the source of the fuel from utility-suppliedelectricity to on-site photovoltaic power generation. The number ofkW_(DC) of photovoltaic power required to provide 2,329 kWh to power theheat pump can be found as:

$\begin{matrix}{{{PV}{Capacity}{Required}} = {\frac{2,351{kWh}/{yr}}{1,400{kWh}/{yr}} = {1.68{kW}_{DC}}}} & (31)\end{matrix}$

Expected photovoltaic production can be forecast, such as described incommonly-assigned U.S. Pat. Nos. 8,165,811; 8,165,812; 8,165,813, allissued to Hoff on Apr. 24, 2012; U.S. Pat. Nos. 8,326,535 and 8,326,536,issued to Hoff on Dec. 4, 2012; U.S. Pat. No. 8,335,649, issued to Hoffon Dec. 18, 2012; U.S. Pat. No. 8,437,959, issued to Hoff on May 7,2013; U.S. Pat. No. 8,577,612, issued to Hoff on Nov. 5, 2013; and U.S.patent application Ser. No. 14/058,121, filed Oct. 18, 2013, pending,the disclosures of which are incorporated by reference.

Finally, as shown in Table 1, Option 2 will cost $14,025. Option 1 isthe minimum unavoidable cost of the two options and will cost $9,000.Thus, the net cost of Option 2 is $5,025. In addition, Option 2 willsave $360 per year in natural gas bills because 60-percent of the $600natural gas bill is for space, which represents a cost avoided. As aresult, Option 2 has a 14-year payback.

TABLE 1 Combined Item Cost Incentive Cost Increasing Ceiling Insulation$300 Replace Ductwork $3,000 Electric-Powered Air Source Heat $10,000Pump (Added Cost) Photovoltaic Power Generation (1.68 $6,720 kW_(DC) @$4,000 per kW_(DC)) Tax Credit for Photovoltaic Power ($1,995)Generation Utility-Offered Whole House Rebate ($4,000) Total $20,020($5,995) $14,025

A building's overall thermal performance can be used to quantify annualenergy consumption requirements by fuel type. The calculations describedsupra assumed that energy prices did not vary with time of day, year, oramount of energy purchased. While this assumption is approximatelycorrect with natural gas and gasoline consumption, electricity prices dovary, with electric rate structures often taking into consideration timeof day, year, amount of energy purchased, and other factors

Overall thermal performance, annual fuel consumption, and otherenergy-related estimates can be combined with various data sets tocalculate detailed and accurate fuel consumption forecasts, includingforecasts of electric bills. The fuel consumption forecasts can be used,for instance, in personal energy planning of total energy-related costsC^(Total), as well as overall progress towards ZNE consumption. FIG. 7is a screen shot showing, by way of example, the graphical userinterface (GUI) 90 of an energy investment choices analysis tool. Totalenergy-related costs C^(Total) include electricity cost (C^(E)), fuelfor heating cost (C^(F)), gasoline (or other automobile fuel) cost(C^(G)), and maintenance cost (C^(M)), as described supra with referenceto Equation (1), or for other energy planning purposes. Through theupper section 91 of the GUI 90, a user can select current and plannedenergy-related equipment and parameters. As applicable, the equipmentand parameters are evaluated in light of current energy data, includingconsumption data, building thermal characteristics, and historical solarresource and weather data, from which proposed energy data can begenerated as investment analysis results in the lower section 92 of theGUI 90.

For instance, in the lower left-hand corner, current 93, proposed 94,and proposed after PV 95 energy consumption statistics are provided.These energy consumption statistics reflect energy costs incurred fortransportation, space heating, water heating, and other electricaldevices, such as lighting, appliances, and electrical devices. Inaddition, net energy consumption 96, which is net electricityconsumption based only upon the energy purchased from the power utility,that is, provided from a source external to the building, and proposedphotovoltaic power production 97, are provided, albeit in a traditional“before” and “after” manner, where current energy consumption 93 isfirst improved through increased energy efficiencies, as reflected bythe proposed energy consumption 94, and later improved through theaddition of on-site photovoltaic power generation 95. Utility-providednet energy consumption 96 statistics, though, can mask the overallefficiency of a building, particularly where on-site power generationhas been installed first, as further described infra beginning with FIG.10 et seq. Where photovoltaic power generation has already beeninstalled, current energy consumption 93 would instead include both netenergy consumption 96 and (already-installed) photovoltaic powerproduction 97 to yield a combined indication of gross energy consumptionupon which other types of energy investment choices, such as replacing agasoline-fueled vehicle with an electrical vehicle, can be considered inthe proper context of overall energy consumption.

The forecasts can be used to accurately model one or more energy-relatedinvestment choices, in terms of both actual and hypothesized energyconsumption and, in some cases, on-site energy production. The energyinvestment choices analysis tool described with reference to FIG. 7 canbe implemented through software. FIG. 8 is a process flow diagramshowing a computer-implemented method 100 for evaluating potentialenergy investment scenarios from a user's perspective, in accordancewith one embodiment. Execution of the software can be performed on acomputer system, such as further described infra with reference to FIG.29 , as a series of process or method modules or steps. The userinteractively inputs energy-related investment selections and can viewanalytical outputs through a graphical user interface.

As an initial step, using the GUI 90, a user makes selections 101 ofenergy-related equipment investments and parameters in the form ofenergy-consuming or (on-site) energy-producing equipment that arecurrently owned or that are under consideration for acquisition. Theanalysis tool helps the user to explore the various aspects of the totalenergy-related costs C^(Total) in terms of price and quantity, asdescribed supra with reference to Equation (2). If the user isinterested in just determining incurred capital cost or forecasting anelectric bill, the user need only enter information about existingequipment. If an energy equipment investment is being considered, theuser will need to select both the equipment currently in use and theequipment proposed to replace or upgrade the current equipment. Notethat the term “equipment” as used in the context of the analysis toolnon-exclusively includes multi-component systems, machinery, fixtures,appliances, and building structure, materials and components, any ofwhich could form the basis of an energy-related investment.Additionally, the term “parameters” refers to aspects of an investmentrelated more to operational use, than to the nature of the equipmentproper. For instance, energy consumption of a fixture, such as lighting,may be reduced by parametrically decreasing the hours of operation, inaddition to (or in lieu of) choosing a more energy-efficient form oflighting fixture.

A pair of databases respectively store listings of equipment 104 andtheir prices 105. The two databases 104, 105 could be combined into asingle database. In addition, the information stored in the twodatabases 104, 105 is expected to be continually evolving and can besupplemented or revised with new data through automatic or manualupdates, which allows the analysis tool to model personal energy-relatedequipment that is new to the market and other kinds of changes.

Each listing in the equipment database 105 lists a type of equipment andthe type of fuel used, including, for example, electricity, heating gasor oil, gasoline (or diesel), or solar. The user makes selections ofequipment for both current and proposed personal equipment investments.Each equipment listing also includes energy-related characteristics,including classifying each listed equipment as affecting one or more ofpersonal electricity cost, heating cost, transportation cost, ormaintenance cost; and an energy affect that can be quantitativelyexpressed as measures of one or more of personal energy-consumption,energy-conservation, or (on-site) energy-production. For instance, anon-EV (electric vehicle) car consumes gasoline (or diesel) and theenergy affect can be expressed as average miles per gallon. The annualor periodic cost of fuel can thus be projected by multiplying annual orperiodic mileage by the average miles per gallon. Note that some typesof equipment neither consume nor produce energy, such as different kindsof building envelope investments, which indirectly conserve energy bypreventing infiltration of ambient conditions. However, theirenergy-related affect can be indirectly expressed based on insulativecontributions to a building envelope, from which a cost (or savings) canbe derived. As well, each equipment listing specifies energy-related andgeneral characteristics that include, as applicable, name; model number;model year; fuel type: and energy (fuel) consumption, conservation orproduction characteristics, operational parameters, and other relatedperformance specifications. Equipment information for energy investmentsthat specifically affect building envelope, furnace, and heat deliveryand suitable for use in the equipment database 105 is described infrawith reference to FIG. 9 . Other equipment information could also beincluded in each listing. The equipment database 105 can include:

-   -   1. Electricity-related equipment investments, including        lighting, appliances, and other devices that consume        electricity.    -   2. Building envelope equipment investments, including windows,        window shades, ceiling and wall insulation, radiant barriers,        roof ridge vents, and other fixtures that conserve energy within        a building envelope.    -   3. Space conditioning equipment investments, including natural        gas furnaces, air conditioning units, heat pumps, stand-alone        heaters, and other units that consume energy for space        conditioning.    -   4. Water heating equipment investments, which can either be        units that consume energy or conserve energy for heating water.    -   5. Vehicle and transportation equipment investments, which can        be conveyances or use of conveyances that consume energy for        transportation, conserve energy for transportation, or both, as        in the case of a hybrid automobile.    -   6. On-site energy producing equipment investments relating to        source of electricity, including photovoltaic power generation,        or, less commonly, small wind, small hydroelectric, or other        distributed or standalone power generation technologies, all of        which produce electricity.        Other types of equipment are possible.

Each listing of price in the equipment prices database 105 correspondsto a listing of equipment in the equipment database 105 and includes, asapplicable, cost of acquisition, whether by purchase, lease, rental, orother form; installation cost; maintenance cost; costs of ownership,such as annual registration, emissions compliance, and taxes; rebates,discounts, or other incentives; and, optionally, current valuation, suchas depreciated value, residual value, resale value, trade-in value, orsalvage value. Other price information could also be included.

Based upon the types of energy-related investments selected, up to threesets of current data 102 may be maintained. First, for all investments,current electricity, fuel, and gasoline consumption data 106 arecollected for each equipment selection 101 for a recent time period,which will generally be for the past year. The consumption data 106 isformed into time series, which is particularly important for electricityand fuel, specifically, fuel used for space conditioning and waterheating. The source, quantity, and type of consumption data will dependupon the nature of the equipment selection. For instance, netelectricity consumption is available from power utility bills, althoughthe amount of electricity consumed for a particular purpose, such asspace or water heating, would need to be identified or estimated fromnet consumption. In a further embodiment, where a consumer has alreadymade a switch to an alternative energy source (or knows with specificitythe expected amount of energy to be provided by an alternative energysource), such as on-site photovoltaic power generation, the netelectricity consumption data is combined with on-site power generation(and consumption) to yield gross energy load, as further described infrawith reference to FIG. 17 . Fuel consumption depends upon the form ofdelivery. Bulk fuels, such as heating oil, are delivered en masse to anon-site tank; for analysis purposes, consumption can be equated toamount purchased. Consumption of metered fuels, like natural gas, isalso available from fuel bills and, like electricity, use for a specificpurpose, may need to be identified or estimated, such as described suprawith reference to Equation (10) for the case of fuel for space heating.Gasoline (or diesel) consumption can be estimated by dividing annualmiles driven by average miles per gallon, or similar metric.

Second, when the proposed energy investments relate to changes to thebuilding's thermal envelope, the thermal characteristics 107 of thebuilding are collected. The overall thermal properties of a building(UA^(Total)) may already be available from an energy audit, or could bedetermined using the empirical approach described supra with referenceto FIG. 4 .

Third, when the proposed energy investments relate to on-site energyproduction, historical solar resource, if photovoltaic energy productionis being considered, and weather data 108 are collected for the samerecent time period as the consumption data 106. In addition, ifnecessary, the historical solar resource and weather data 108 areconverted into time series using the same time resolution as applicableto the consumption data 106. Weather data can be obtained from weatherreporting services. Solar resource data is discussed in further detailinfra. The equipment selections 101 are combined with the current data102 to generate proposed data 103 for indicating annual consumption 109,by fuel type, which are calculated for both the equipment currently inuse and the equipment proposed for use to replace or upgrade the currentequipment. Fuel consumption and gasoline (or diesel) consumption areconverted into electricity-equivalent units, as further described infra.The electricity consumption time series data is submitted to a billcalculator 110 and is combined with electric rate structure informationto calculate an estimated annual cost 112. The estimated annual cost 112is combined with the electricity-equivalent units to forecast a totalannual cost, and the initial capital cost is compared to the totalannual cost to determine an estimated system payback 113.

From a non-technical person's perspective, a sufficient amount ofinformation is presented in a single screen to help a consumer in makinginformed energy investment decisions. FIG. 9 is a detail of the GUI 90of FIG. 7 showing, by way of example, an annotated graph 120 of powerconsumption. The x-axis 121 represents time. The y-axis 122 representspower, expressed in kW. Both current power consumption 123, which islimited to net electricity consumption based only upon the energypurchased from the power utility, that is, provided from a sourceexternal to the building, and proposed power consumption 124, followingthe implementation of energy efficiencies and installation of on-sitephotovoltaic power generation, are depicted, respectively based on theelectricity demand profiles for the current and proposed investments.Proposed power consumption 124 reflects the effect of electric vehicle(“EV”) charging; operation of water and space heating pumps; efficiencyinvestments in the form of load reduction achieved by replacing existingconstant load, “Always On” electric devices with more energy efficientelectric devices and modifying operating schedule parameters; and fuelswitching from natural gas, supplemented with on-site photovoltaic powergeneration.

Power utilities and energy agencies have become increasingly proactivein assisting their customers with making informed energy investmentdecisions and by urging their customers to lower their energyconsumption through improved efficiency and adoption of renewable energysources. To help educate customers, they often provide periodic energyconsumption statistics, which reflect the net energy purchased from theutility. FIG. 10 is a graph showing, by way of example, monthly netenergy consumption statistics 130. The x-axis 131 represents months andthe y-axis 132 represents electricity consumption, expressed in kilowatthours (kWh). Net electricity usage 133 is plotted for each month. Netelectricity usage 133 represents energy purchased from a power utility,which invariably implies energy provided from a source external to thebuilding, as opposed to energy generated (and consumed) on-site.Frequently, such monthly net energy consumption statistics are providedby power utilities or energy agencies to their customers throughinformational Web sites and printed form. In this Web page example, apull down menu enables a user to view electricity consumption by utilitybill 134, which also corresponds to each month of consumption over thepast twelve months. Other types of user input controls are possible.Here, the energy consumer both purchases electricity from a powerutility and generates electricity on-site with a photovoltaic powergeneration system. The net usage 133, though, only reflects the netamount of energy purchased from the power utility; energy generated (andconsumed) on-site is implicitly included in the monthly net energyconsumption statistics by virtue of a lowering of the amount of energypurchased.

The effect of implicitly including on-site energy generation can bemisleading to the consumer because the monthly net energy consumptionstatistics only provide a partial picture of total energy consumption.The consumption of energy generated on-site decreases the net amount ofenergy that must be purchased from the utility, yet based on theutility's periodic energy consumption statistics, the consumer remainsunaware of how much on-site energy was consumed during the samereporting period. Inefficiencies in home energy consumption areeffectively masked from view. Here, during the late spring through earlyfall months, photovoltaic power generation contributes significantly tothe gross energy available for home consumption, which creates negativenet usage 133. During the winter months, energy consumption reflects asubstantial seasonal increase, which, in most cases, could be expected,as heating fixtures, specifically, furnaces, will consume significantamounts of energy, while photovoltaic power generation can suffer aseasonal decline in output.

Such periodic energy consumption statistics can send a mixed message. Ifa consumer sees a lowered monthly energy bill, the consumer may believethat they have succeeded in lowering their energy consumption. However,a lower monthly energy bill may not necessarily be due to improvedefficiency in those situations where the consumer has also implementedan on-site renewable energy source that lowers a consumer's dependenceon utility-supplied energy, and thus lowers their monthly energy bill.

Monthly net energy consumption bins together daily electricity use intoapproximately 30-day intervals. Finer-grained energy consumptionstatistics can help a consumer better identify energy wasting habits.FIG. 11 is a graph showing, by way of example, average daily net energyconsumption statistics 135, including on-site photovoltaic powergeneration. The x-axis 136 represents months and the y-axis 137represents average daily electricity consumption, expressed in kilowatthours per day (kWh/day). Average daily net electricity usage 138 isplotted for each month with energy generated on-site included. In thisWeb page example, the pull down menu enables the user to viewelectricity consumption by average day 139. Here, net usage 138 showsscaled down negative net usage during the late spring to early fallmonths as the energy consumption requirements of the building are met(and exceeded) by the on-site photovoltaic power generation. A similarlyscaled down increase in net energy consumption occurs during the wintermonths.

With only monthly net energy purchases reflected, the net usage 133 maycreate a misperception that a home is energy efficient, as other formsof inefficiencies, such as large “vampire” loads, are effectivelydisguised. (Vampire loads refer to the electricity consumed byappliances while they are switched off or in a standby mode. Forexample, a remote control receiver or a text or light display stillconsumes electricity, even though the appliance is turned off and notperforming its primary function.) FIG. 12 is a graph showing, by way ofexample, average daily gross energy consumption statistics 140,excluding on-site photovoltaic power generation. The x-axis 141represents months and the y-axis 142 represents average dailyelectricity consumption, expressed in kilowatt hours per day (kWh/day).Average daily gross energy load 143 is plotted for each month. In thisWeb page example, a pair of pushbuttons 144 enable the user to viewelectricity consumption by either net load 145, which includes on-sitephotovoltaic power generation, or gross load 146 (selected). Other typesof user input controls are possible. Gross energy load 143 combines boththe net energy purchased from the power utility and estimated net energygenerated (and consumed) on-site by photovoltaic power generation, asfurther described infra with reference to FIG. 17 . Here, the differencebetween the lowest and highest average daily net load is only about fivekWh/day, yet peak average usage occurs in the winter, as expected, aswell as in June and August. Depiction of the gross energy load 143 showsthat energy consumption is fairly consistent throughout the year,particularly when the slightly higher energy consumptions caused bysummertime cooling and wintertime heating are factored out. The trueaverage daily energy consumption is exposed, and the need to makeimprovements in energy conservation are more readily understood by theconsumer, especially as the contributions to gross energy loadattributable to on-site photovoltaic power generation as opposed toutility-supplied energy do little to lower the overall amount of energyconsumed, independent of seasonal changes in power generation output.

The average daily gross energy consumption statistics, such as shown inFIG. 12 , can be supplemented with energy investment planning tools,such as shown in FIG. 7 , to help customers find ways to improve theirenergy efficiency, which can be particularly persuasive when provided toa customer through an interactive informational Web site. FIG. 13 is agraph showing, by way of example, average daily gross energy consumptionstatistics 147, excluding on-site photovoltaic power generation withlight emitting diode (LED) lighting fixtures and lighting usagereduction. The x-axis 148 represents months and the y-axis 149represents average daily electricity consumption, expressed in kilowatthours per day (kWh/day). Average daily gross energy load 150 is plottedfor each month. In this Web page example, a pair of option boxes 151enable the user to view electricity consumption with an electric vehicle(EV) 152 in place of a gasoline-powered vehicle and light emitting diode(LED) fixtures in place of conventional lighting, plus energy usagepattern reductions 153 (selected). Other types of user input controlsare possible. Here, switching to LED fixtures and reducing energyconsumption by turning off unnecessary lights and curtailing wastefulhabits decreases average daily electricity by about ten kWh/day, whichamounts to an average decrease of about 50% per day.

Overall energy consumption can be decreased by replacing inefficientforms of transportation with electric-powered vehicles. FIG. 14 is agraph showing, by way of example, average daily gross energy consumptionstatistics 154, excluding on-site photovoltaic power generation withelectric vehicle usage. The x-axis 155 represents months and the y-axis156 represents average daily electricity consumption, expressed inkilowatt hours per day (kWh/day). Average daily gross energy load 147 isplotted for each month. Although recharging an electric vehiclenoticeably increases monthly electricity consumption, when viewed on aholistic level with respect to all forms of energy consumed annually,replacing a gasoline-powered vehicle with an electric vehicle actuallysaves a significant amount of energy annually, as further explainedinfra beginning with FIG. 22 .

When the option boxes 151 for an electric vehicle 152 and light emittingdiode fixtures, plus energy usage pattern reductions 153 are bothselected, average daily gross energy load is only slightly higher thanthe gross energy load, such as shown in FIG. 12 , without any energyconservation steps. FIG. 15 is a graph showing, by way of example,average daily gross energy consumption statistics 158, excluding on-sitephotovoltaic power generation with light emitting diode lightingfixtures, lighting usage reduction, and electric vehicle usage. Thex-axis 159 represents months and the y-axis 160 represents average dailyelectricity consumption, expressed in kilowatt hours per day (kWh/day).Average daily gross energy load 161 is plotted for each month. Theenergy costs for recharging the electric vehicle are effectivelyabsorbed by the light emitting diode fixtures and energy usage patternreductions, while the costs of gasoline are entirely avoided. Finally,FIG. 16 is a graph showing, by way of example, average daily net energyconsumption statistics 158, including on-site photovoltaic powergeneration with light emitting diode lighting fixtures, lighting usagereduction, and electric vehicle usage. The x-axis 159 represents monthsand the y-axis 160 represents average daily electricity consumption,expressed in kilowatt hours per day (kWh/day). Average daily net energyload 161 is plotted for each month. The differences in average dailyload before switching to an electric vehicle and LED fixtures, plusimproved energy usage patterns, such as shown in FIG. 11 , and after areminimal.

Gross energy load is determined by combining net electricity consumptiondata, such as provided by a power utility or energy agency, with on-sitepower generation, such as photovoltaic power generation, as producedover the same time period. FIG. 17 is a process flow diagram showing aroutine 170 for estimating gross energy load for use in the method 100of FIG. 8 . The process is explained with reference to photovoltaicpower generation and can be applied mutatis mutandis to other types orcombinations of on-site renewable energy sources, including small wind,small hydroelectric, or other distributed power generation technologies.

Net load data is first obtained for a known time period (step 171).Typically, net load data is provided by a power utility or energy agencyin increments of one month. Daily average net load can be estimated bytaking an average of the net load data over a 30-day or otherappropriate time period.

Photovoltaic production data is then simulated for the customer'slocation with the same time resolution as each point of net load data(step 172), whether based on monthly consumption, average dailyconsumption, or other consumptive time period. The simulation must beperformed using time- and location-correlated solar resource data, aswell as specific information about the orientation and othercharacteristics of the photovoltaic system, such as can be provided bythe Solar Anywhere service (http://www.SolarAnywhere.com), a Web-basedservice operated by Clean Power Research, L.L.C., Napa, Calif. Theoperational specifications of the photovoltaic system may be availablefrom the manufacturer or installer. Otherwise, the operationalspecifications can be inferred through evaluation of historical measuredsystem production data and measured solar resource data, such asdescribed in commonly-assigned U.S. Pat. No. 8,682,585, issued to Hoffon Mar. 25, 2014, or with net load data and measured solar resourcedata, such as described in commonly-assigned U.S. Pat. No. 9,880,230,Issued Jan. 30, 2018, the disclosures of which are incorporated byreference. The simulated photovoltaic production data can be normalizedto a daily average by taking an average over the same 30-day (or otherappropriate) time period as used with the net load data.

Briefly, the photovoltaic production data is simulated by firstobtaining a time series of solar irradiance data for a set of locationsrepresentative of the geographic region within which the building islocated. Each time series contains solar irradiance observationselectronically recorded at fixed time intervals over successive timeperiods. The solar irradiance observations can include direct irradiancemeasured by a representative set of ground-based weather stations, whichare assembled as point statistics as an average of all values of rawmeasured irradiance. The solar irradiance observations can also includeinferred irradiance based on power statistics collected for existingphotovoltaic systems. Apparent irradiance is inferred as area statisticsbased on a performance model selected for each of the systems and thetime series of power statistics. Finally, the solar irradianceobservations can include area solar irradiance observations based on aset of pixels from satellite imagery for the geographic region in whichthe building is located. The area solar irradiance statistics are firstconverted into irradiance statistics for an average point within the setof pixels and measured irradiance is determined as average pointstatistics as an average of all values of the set of pixels. Othersources of the solar irradiance data are possible.

Next, the solar irradiance data in the time series is converted overeach of the fixed time intervals, such as at half-hour intervals, into aset of clearness indexes, which are calculated relative to clear skyglobal horizontal irradiance. The set of clearness indexes areinterpreted as irradiance statistics. A time lag correlation coefficientfor an output time interval can also be determined to enable thegeneration of an output time series at any time resolution, even fasterthan the input data collection rate. The time lag correlationcoefficient captures the relationship between the power output by thephotovoltaic system at one point of time and the power output by thephotovoltaic system at one time interval later.

Finally, a time series of the power statistics for the photovoltaicsystem is generated as a function of the irradiance statistics and thephotovoltaic system's operational specification, including power rating.The resultant high-speed time series performance data can be used topredictably estimate power output and photovoltaic productionvariability.

The high resolution time series of power output data is determined inthe context of a photovoltaic fleet, whether for an operational fleetdeployed in the field, by planners considering fleet configuration andoperation, or by other individuals interested in photovoltaic fleetvariability and prediction. Time series power output data for aphotovoltaic fleet is generated using observed field conditions relatingto overhead sky clearness. Solar irradiance relative to prevailingcloudy conditions in a geographic region of interest is measured. Directsolar irradiance measurements can be collected by ground-based weatherstations. Solar irradiance measurements can also be inferred by theactual power output of existing photovoltaic systems. Additionally,satellite observations can be obtained for the geographic region. Boththe direct and inferred solar irradiance measurements are considered tobe sets of point values that relate to a specific physical location,whereas satellite imagery data is considered to be a set of area valuesthat need to be converted into point values, such as described incommonly-assigned U.S. Pat. Nos. 8,165,811; 8,165,812; 8,165,813, citedinfra. Still other sources of solar irradiance measurements arepossible.

The net load data and simulated photovoltaic production data are thencombined at each point in the known time period (step 173) to yieldgross energy load 174. Gross energy load is expressed in kilowatt hours,although other units of energy could be used. The gross energy load canthen be presented in graphical form, such as described supra withreference to FIG. 12 to FIG. 15 , or in other written form.

The effects current and proposed energy investments and reductions areultimately reflected as a payback on investment, which helps to providea consumer with answers on personal energy consumption and anunderstanding what options and alternatives work best for the consumer'senergy needs. FIG. 18 is a process flow diagram showing a routine 180for evaluating potential energy investment payback for use in the method100 of FIG. 8 . The process uses the equipment selections 101 incombination, as applicable, with current electricity, fuel, and gasolineconsumption data 106; building thermal characteristics 107; andhistorical solar resource and weather data 108.

By way of example, potential energy investments that affect electricitycost (C^(E)), fuel for heating cost (C^(F)), and gasoline (or otherautomobile fuel) cost (C^(G)), per Equation (1), as discussed supra, aremodeled, but other costs, including maintenance cost (C^(M)), could alsobe weighed in the evaluation of total energy-related costs C^(Total).Initially, as applicable, an initial capital cost 185, as discussedsupra, and annual consumption, by fuel type, are calculated (step 181).The annual consumption values are determined for both the equipmentcurrently in use and the equipment proposed to replace or upgrade thecurrent equipment. In this example, the total energy-related costsC^(Total) include gasoline (or other automobile fuel) cost (C^(G)), sothe energy consumed by the person's mode of transportation isdetermined. This example assumes that the form of transportation is apersonal car. Other forms of transportation are possible, such astrains, buses, bikes, walking, and so forth.

TABLE 2 Vehicle Fuel Consumption Current Proposed Annual Mileage 12,00012,000 Miles Per Gallon 16 129 Vehicle Is Included In Analysis? TRUETRUE Gasoline Consumption (gallons per year) 750 93 Miles Per kWh 0.473.83 Electricity Consumption (kWh per year) 25,275 3,135 Vehicle IsElectric Powered? FALSE TRUE EV Charging Efficiency N/A 85% ElectricityPurchases (kWh-eq. per year) 25,275 3,688 Gasoline Purchases (gallonsper year) 750 0 Electricity Purchases (kWh per year) 0 3,688

Referring to Table 2, the consumer currently drives a 2004 Honda OdysseyEX minivan about 12,000 miles per year primarily for city driving. Forthis type of usage, the vehicle has a stated fuel economy of 16 milesper gallon and will consume 750 gallons of gasoline annually. There are33.7 kWh of energy per gallon of gasoline, so the vehicle's annual fuelconsumption represents an electricity-equivalent of 25,275 kWh annually.

The consumer is proposing to replace the current vehicle with a 2013Nissan Leaf SV, which is plug-in charging all-electric vehicle. The LeafSV achieves a gasoline-equivalent of 129 miles per gallon for citydriving, which converts to 3.8 miles per kWh. An inefficiency occurswhen the vehicle is charged, which can be assumed to be around percent.For the same type of usage, about 12,000 miles per year primarily forcity driving, the Leaf SV, at 3.8 kWh per mile with an 85 percentcharging efficiency, would require 3,688 kWh annually, which comparesquite favorably to the electricity-equivalent of 25,275 kWh used by theOdyssey EX under identical driving conditions.

Electric energy efficiency investments reduce annual electricityconsumption. In every building, there is typically some percentage ofelectricity drawn on a continuous basis by devices that are alwaysturned on. These constant load devices may be, for example, electric hotwater heaters, clocks, electric timers for operating lights,uninterruptible power supplies for computer equipment, and appliancesplaced on a standby mode.

The electric load consumed by “Always On” devices can be reduced byreplacing existing “Always On” electric devices with more energyefficient electric devices and modifying operating schedule parametersor by unplugging unused devices. Referring to Table 3, a reduction in“Always On” loads from 150 Watts to 50 Watts translates to a savings of876 kWh per year [(0.15 kW−0.05 kW)×8,760 hours].

In addition, other electric efficiency investments are possible, such asenergy efficient appliances and efficient lighting. In this example,replacing fifty 15-Watt CFLs with 6-Watt LEDs that are operated for onlysix hours per day translates to a savings of 986 kWh per year [50×(0.015kW−0.006 kW)×(6 hours per day)×(365 days per year)].

TABLE 3 Electrical Efficiency Savings and Capital Cost Savings (kWh/yr)Savings (kWh/hour) Cost Always On Loads 876 0.10 $0 Lights 986 0.11 $250Total 1,862 0.21 $250

Improvements to a building can change the overall thermal performance ofthe building UA^(Total) Improvements can affect how heat loss or gainoccurs by conduction through each unique building surface and throughinfiltration. In Equation (42), as further described infra, theseeffects can be calculated by incrementally changing the building'sthermal characteristics. Referring to Table 4, the house in this examplehas R-6 wall insulation, that is, insulation with an R-value of 6.Adding R-13 insulation increases the overall insulation to R-19. Thechange in UA^(Total) for 225 ft² of R-19 insulation equals 26 Btu/hr-°F. [(⅙− 1/19)×225]. The total of all UA^(Total) changes equals 218Btu/hr-° F.

TABLE 4 Building Improvements Current Proposed Area Change R-Value (ft²)Cost in UA Wall Insulation 6 19 225 $60 26 Attic Insulation 13 26 900$266 35 Window Insulation 2 6.7 319 $4,500 112 ACH @ Volume StandardPressure (ft²) Cost Seal Building 0.25 0.15 25,500 $100 46 TotalBuilding $4,926 218 Improvement

Several ratios are calculated based on current and proposed efficienciesand UA^(Total) values, as further discussed infra with reference toEquation (38), Equation (42), and Equation (43). Referring to Table 5,the efficiency ratio equals the current value divided by the proposedvalue. The relationship is reversed for the UA^(Total) values, where theUA^(Total) ratio equals the proposed UA^(Total) value divided by thecurrent UA^(Total) value. The current UA^(Total) value of the buildingis a required input and can be obtained by the empirical approachdescribed supra with reference to FIG. 4 . The efficiency ratios inTable 5 will now be discussed.

TABLE 5 Efficiencies Current Proposed Ratio Water Heating Energy Factor62% 245% 25% Building UA (Btu/hr-° F.) 583 365 63% Duct Efficiency 77% 94% 82% Furnace Efficiency 80% 249% 32% Total Space Heating (UA *Ducts * Furnace) 16%

The Water Heating Energy Factor Ratio is used to determine the proposedtotal annual energy required for water heating. Current annual waterheating fuel consumption was calculated using the approach summarized inEquation (12), which is 199 therms of natural gas. There are 3,412 Btuper kWh. Thus, the current consumption of fuel for water heating can beexpressed as 5,820 kWh of natural gas. The proposed consumption of fuelfor water heating equals 5,820 kWh times the Water Heating Energy FactorRatio and is 1,473 kWh per year (5,820×0.25). Referring to Table 6, theinstalled cost for the heat pump water heater is $1,899.

TABLE 6 Water Heating Capital $1,199 Installation $700 Total Cost $1,899

Space heating requirements are calculated in a two-step process. Thesizing of the heating source is first estimated, after which cost can bedetermined. One approach to sizing the heating source is provided inManual J, cited supra. However, that sizing approach does not take intoaccount historical information about the building's consumption nor isthe sizing approach dynamic.

Here, an alternate approach to sizing of the heating source is applied.First, historical fuel consumption requirements are evaluated todetermine worst-day situations, rather than simply assuming worst dayconditions. Second, the approach dynamically incorporates the effect ofinvestment decisions across technologies and fuel types and theirvarious interactions. For example, the decision to add insulating windowshades reduces a building's rate of heat loss and thus reduces therequired size of the space conditioning heat pump, which, in turn,reduces capital cost. This decision also reduces the total amount ofheat that needs to be provided by the heat pump, which, in turn, reducesthe size of the photovoltaic system needed to supply energy to the heatpump. These interactions are automatically calculated.

Referring to Table 7, the maximum daily natural gas purchased for thebuilding in this example for space heating purposes, as determined usingdaily water heating consumption from Equation (12) combined with totaldaily natural gas purchases, was 5.71 therms. In other words, the peakday over the year analyzed required a purchase of 5.71 therms of naturalgas. Based on the proposed energy investments, the building envelope andduct losses will respectively be lowered to 63 percent and 82 percent,per Table 5. The product of these two ratios is 51 percent, which meansthat proposed energy investments would require 2.93 therms on the worstday, assuming the same furnace efficiency, η^(Furnace). 48,836 Btu ofnatural gas must be purchased per hour, given a maximum daily operationof six hours. Since the current furnace is 80 percent efficient, 39,069Btu of heat are actually delivered per hour.

The proposed space heating source is a heat pump that has a HeatingSeason Performance Factor (HSPF) of 8.5 Btu/Wh, which means that theheat pump will consume 4.6 kW per hour (39,069 Btu/8,500 Btu/kWh). Therating of this heat pump can also be expressed in tons by dividing by12,000. The cost for the heat pump equals the product of the rating,expressed in in tons, times the cost, expressed in dollars per ton, plusthe fixed cost, installation cost, and ductwork cost. The total proposedspace heating cost is $11,256.

TABLE 7 Space Heating Sizing UA Ratio * Current Duct Ratio Proposed MaxDaily Consumption 5.71 51% 2.93 (therms/day) Max Daily Operation (Hours)6 6 Max Hourly Operation 95,242 48,836 (Btu/hour) Delivered Heat(Btu/hour) 76,193 39,069 Furnace HSPF (Btu/Wh) 8.50 Furnace AFUE 0%Furnace Is Heat Pump TRUE Max Hourly Space Heating Consumption (kW/hr)4.60 Max Hourly Space Heating Consumption (tons) 3.26 Space Heating CostRequired Tons Cost per Ton Cost Capacity Cost 3.26 $1,000 $3,256 FixedCost $3,000 Capacity + Fixed Cost $6,256 Installation Cost $2,000 DuctCost $3,000 Total Cost $11,256

Installing a photovoltaic system allows a consumer to offset purchasedelectricity consumption with on-site power generation. In theinteractive energy investment choices analysis tool, the consumer couldsimply explicitly size the photovoltaic system. Alternatively, theconsumer can specify the percentage of purchased electricity consumptionto offset by on-site power generation.

Referring to Table 8, in this example, annual consumption is estimatedat 9,682 kWh. The consumer has indicated that the photovoltaic systemshould provide 80 percent of annual consumption, or 7,746 kWh.Historical photovoltaic power production was analyzed for the locationand time period of interest. Here, a 1-kW-DC, south-facing photovoltaicsystem would produce 1,521 kWh per year; however, a 5.09 kW-DCphotovoltaic system is needed to produce 7,746 kWh. A photovoltaicsystem of this capacity would cost $20,376 and would be eligible toreceive 30-percent federal tax credit of $6,113.

TABLE 8 PV System Sizing and Cost Proposed Consumption (kWh/yr) 9,682Percent Cons. to be Supplied by PV 80% PV Supplied Energy (kWh/yr) 7,746Historical Production (kWh/kW-DC/yr) 1,521 Required PV Size (kW-DC) 5.09Per Unit PV Cost ($/kW) $4,000 Total PV Cost $20,376 Federal Tax Credit$6,113

Referring back to FIG. 10 , annual electric consumption is thenconverted into time series consumption (step 182), which allocatesannual electric consumption into time-series values on an hourly, orother time interval, basis. For any particular end-use, the distributionof annual energy must satisfy the requirement that the sum of all 8,760hours in a year (or all 8,784 hours in a leap year), as factored, equals1, in accordance with:

$\begin{matrix}{{\sum\limits_{m = 1}^{12}{\sum\limits_{d = 1}^{28{to}31}{\sum\limits_{h = 1}^{24}{hf}_{m,d,h}}}} = 1} & (32)\end{matrix}$

where m, d, and h respectively represent month, day, and hour; and hfrepresents the percent of total annual energy being consumed in a givenhour. A daily factor for each month and day is defined, such that thesum of the daily factors for a particular month and day equals:

$\begin{matrix}{{df}_{m,d} = {\sum\limits_{{Hour} = 1}^{24}{hf}_{{h❘m},d}}} & (33)\end{matrix}$

where hf_(h|m,d) signifies the hourly factor for hour h, given month mand day d.

A new term, called normalized hourly factors, is defined, which equalsthe original hourly factor divided by the daily factor for that monthand day, expressed as:

h ❘ m , d = hf h ❘ m , d df m , d ⁢ for ⁢ h = 1 ⁢ to ⁢ 24 ( 34 )

Rearranging Equation (34) and substituting into Equation (32) yields:

∑ m = 1 12 ∑ d = 1 28 ⁢ to ⁢ 31 df m , d ⁢ ∑ h = 1 24 h ❘ m , d = 1 ( 35 )

Repeat the same process to define a daily factor/monthly factorrelationship:

∑ m = 1 12 mf m ⁢ ∑ d = 1 28 ⁢ to ⁢ 31 d ❘ m ∑ h = 1 24 h ❘ m , d = 1 ( 36)

The benefit of Equations (35) and (36) is that they can be used tocreate load profiles for which detailed hourly data is unavailable.Suppose, for example, that total daily water heating consumption isavailable for each day of the year, but hourly data are unavailable. Inthis case, the consumption profiles distribution within any given day ofthe year could be assumed to be the same as every other day, as would bethe case if the status of the water heater was always either on or offduring the same time of the day. This assumption does not require thatthe total water heater load be the same for every day of the year.

Here, Equation (35) simplifies to the following equation:

∑ m = 1 12 ∑ d = 1 28 ⁢ to ⁢ 31 df m , d ⁢ ∑ h = 1 24 h = 1 ( 37 )

Equation (37) can be used in the context of current Green Button naturalgas data. A similar approach can be taken to define constant loadprofiles for a day within a given month.

The hourly distribution factors for a proposed energy investmentscenario can be depicted. FIG. 19 is a graph depicting, by way ofexample, assumed hourly distribution factors, as used in the routine ofFIG. 8 . The x-axis represents time of day. The y-axis representspercentage. The assumed hourly distribution factors in the example forwater heating, space heating, and electric vehicle charging are used inthis example. Electric vehicle charging is assumed to follow the samepattern every day of the year. The daily factors for the water and spaceheating are based on measured natural gas purchase data. Table 9presents projected hourly electricity consumption by end-use for oneday. The columns present electricity by Other Consumption, WaterHeating, Space Heating, and EV Charging. The sum of these four columnsis Total Consumption.

TABLE 9 Projected Hourly Electricity (KWh) Other Water Space EV Total PVNet Rate Structure Information DST Start Time Consumption HeatingHeating Charging Consumption Production Consumption Season Period RateCost 1/1/13 12:00 AM 0.32 0.00 0.0 2.02 2.34 0.00 2.34 Winter Off Peak$0.10 $0.24 1/1/13 1:00 AM 0.42 0.00 0.0 2.02 2.44 0.00 2.44 Winter OffPeak $0.10 $0.25 1/1/13 2:00 AM 0.85 0.00 0.0 2.02 2.87 0.00 2.87 WinterOff Peak $0.10 $0.29 1/1/13 3:00 AM 0.87 0.00 0.0 2.02 2.89 0.00 2.89Winter Off Peak $0.10 $0.29 1/1/13 4:00 AM 0.85 0.00 0.0 2.02 2.87 0.002.87 Winter Off Peak $0.10 $0.29 1/1/13 5:00 AM 0.85 0.00 2.1 0.00 2.930.00 2.93 Winter Off Peak $0.10 $0.30 1/1/13 6:00 AM 1.21 1.35 2.1 0.004.64 0.00 4.64 Winter Off Peak $0.10 $0.47 1/1/13 7:00 AM 0.85 1.35 2.10.00 4.28 −0.21 4.08 Winter Partial Peak $0.16 $0.66 1/1/13 8:00 AM 1.140.00 2.1 0.00 3.22 −0.98 2.25 Winter Partial Peak $0.16 $0.37 1/1/139:00 AM 0.83 0.00 0.0 0.00 0.83 −1.94 −1.11 Winter Partial Peak $0.16($0.18) 1/1/13 10:00 AM 0.52 0.00 0.0 0.00 0.52 −2.63 −2.12 WinterPartial Peak $0.16 ($0.35) 1/1/13 11:00 AM 0.22 0.00 0.0 0.00 0.22 −3.01−2.79 Winter Partial Peak $0.16 ($0.46) 1/1/13 12:00 PM −0.18 0.00 0.00.00 −0.18 −3.07 −3.25 Winter Partial Peak $0.16 ($0.53) 1/1/13 1:00 PM−0.32 0.00 0.0 0.00 −0.32 −2.81 −3.13 Winter Partial Peak $0.16 ($0.51)1/1/13 2:00 PM −0.13 0.00 0.0 0.00 −0.13 −2.21 −2.35 Winter Peak $0.27($0.63) 1/1/13 3:00 PM 1.18 0.00 0.0 0.00 1.18 −1.41 −0.23 Winter Peak$0.27 ($0.06) 1/1/13 4:00 PM 2.11 0.00 0.0 0.00 2.11 −0.48 1.62 WinterPeak $0.27 $0.43 1/1/13 5:00 PM 1.29 1.35 0.0 0.00 2.64 0.00 2.64 WinterPeak $0.27 $0.71 1/1/13 6:00 PM 1.60 0.00 2.1 0.00 3.68 0.00 3.68 WinterPeak $0.27 $0.99 1/1/13 7:00 PM 1.96 0.00 2.1 0.00 4.04 0.00 4.04 WinterPeak $0.27 $1.08 1/1/13 8:00 PM 0.24 0.00 0.0 0.00 0.24 0.00 0.24 WinterPeak $0.27 $0.06 1/1/13 9:00 PM 0.33 0.00 0.0 0.00 0.33 0.00 0.33 WinterPartial Peak $0.16 $0.05 1/1/13 10:00 PM 0.35 0.00 0.0 0.00 0.35 0.000.35 Winter Partial Peak $0.16 $0.06 1/1/13 11:00 PM 0.72 0.00 0.0 0.000.72 0.00 0.72 Winter Off Peak $0.10 $0.07

Referring back to FIG. 10 , net consumption is calculated usingtime-correlated production data (step 183), which requires combiningtime series total consumption data with time- and location-correlatedproduction data. In many cases, photovoltaic production data may be ofinterest. As a result, historical photovoltaic production data needs tobe simulated for the location of interest. The simulation must beperformed using time- and location-correlated solar resource data, aswell as specific information about the orientation and othercharacteristics of the photovoltaic system, such as can be provided bythe Solar Anywhere service (http://www.SolarAnywhere.com), a Web-basedservice operated by Clean Power Research, L.L.C., Napa, Calif. The timeseries photovoltaic production data is subtracted from the time seriesconsumption data to yield time series net consumption data. Photovoltaicproduction and net consumption for one day are presented in Table 9.

Finally, an electric bill is calculated (step 184), from which annualcost 186 can be forecast and upon which payback 187 can be determined.Electric bill calculation involves combining the net consumption datawith the applicable electric rate structure information, includingdetails about fixed, demand, tier, and time-of-day charges. In Table 9,the right columns present results for one day using a Pacific Gas andElectric EV-A tariff rate structure. Importantly, different rates can beused for “Before” and “After” calculations because a rate switch may befinancially beneficial. The net consumption profile should be runthrough the detailed electric bill calculator for all possible ratestructures to select the one that provides the greatest benefit.

The interactive energy investment choices analysis tool, described suprawith reference to FIG. 7 , provides a consumer with the informationnecessary to evaluate the economic savings or costs of newenergy-related equipment investments for existing buildings. In asimilar manner, energy investments that specifically affect buildingenvelope, furnace, and heat delivery can also be evaluated. FIG. 20 is aflow diagram showing a computer-implemented method for evaluatingpotential energy investment scenarios specially affecting a building'senvelope, heating source, or heating delivery 190, in accordance with afurther embodiment. The method 190 can be implemented in software andexecution of the software can be performed on a computer system, such asfurther described infra with reference to FIG. 29 , as a series ofprocess or method modules or steps.

Initially, the amount of total fuel purchased annually Q^(F) isobtained, which can be found in a utility bill, and the ratio Hof theamount of fuel consumed annually for heating Q^(F-Heating) over theamount of the total fuel purchased annually Q^(F) is calculated (step191). The amount of fuel consumed annually for heating Q^(F-Heating) canbe derived empirically based on the fuel consumed during non-heatingseason months, as described supra with reference to Equation (2), orfrom the building's thermal performance and heating and deliveryequipment characteristics, as described supra with reference to Equation(14) (step 191). The ratio H can be used to identify the initial cost195 of the fuel consumed annually for heating based on the total cost ofthe fuel purchased annually.

To evaluate energy investments mainly affecting heating efficiency ordelivery efficiency, a modified version of Equation (10) can be used.Depending upon the energy investments being evaluated, one or more ofthe existing thermal performance of the building UA^(Total), existingfurnace efficiency η_(furnace), and existing delivery efficiencyη^(delivery) may be needed and can be estimated, if not available (step192). To represent the costs after investment, each variable in Equation(10) that corresponds to a new energy investment is labeled with a caretsymbol ({circumflex over ( )}) (step 193). Equation (15) is substitutedinto the Equation (10), which is then simplified and solved (step 194)to yield the new amount of fuel used strictly for space heating{circumflex over (Q)}^(F-Heating):

Q ^ F - Heating = ( H ) ⁢ ( Q F ) ⁢ ( Total UA Total ) ⁢ ( η furnace η ^furnace ) ⁢ ( η delivery η ^ delivery ) ( 38 )

Note that the variables in Equation (15) do not have caret symbolsbecause the variables represent the values for the existing buildingbefore the investment is made. Based on {circumflex over(Q)}^(F-Heating), the new cost 196 of the fuel consumed annually forheating based on the new energy-related equipment investments can befound, and the investment payback 197 can be evaluated by comparing theinitial cost 195 to the new cost 196.

In Equation (38), the new amount of fuel required for heating{circumflex over (Q)}^(F-Heating) equals the amount of total fuelpurchased annually Q^(F), as fractionally adjusted by the ratio H,multiplied by three additional interrelated ratios, each term in theratio representing, as applicable, characteristics of both existing andproposed equipment:

-   -   New thermal performance of building        ^(Total) divided by existing thermal performance of building        UA^(Total)    -   Existing furnace efficiency η^(furnace) divided by new furnace        efficiency {circumflex over (η)}^(furnace).    -   Existing delivery efficiency η^(delivery) divided by new        delivery efficiency {circumflex over (η)}^(delivery).

Equation (38) is quite useful. For example, suppose that a consumer isconsidering an investment in a new furnace. The existing furnace has an80-percent efficiency η^(furnace) and the delivery system has a78-percent efficiency η^(delivery). If the building had a $1,000 annualbill for fuel required for heating, Equation (38) allows the consumer todetermine the fuel cost for a new 96-percent efficient furnace with95-percent efficient ductwork. Since there is no change to thebuilding's thermal characteristics, Equation (38) suggests that the newannual fuel cost will be $1,000×(0.80/0.96)×(0.78/0.95)=$684.

In addition to assessing the benefits associated with a new furnace anddelivery system, a consumer may want to understand the effect ofbuilding envelope improvements, such as new windows or increasedinsulation, which can be determined by evaluating both the building'soriginal thermal characteristics (UA^(Total)) and its new thermalcharacteristics (

^(Total)). The typical approach to obtaining the existing and newthermal characteristics of a building is to perform a detailed energyaudit that requires fully modeling the building by taking physicalmeasurements of the surface areas of all non-homogeneous exterior-facingsurfaces or verifying non-exposed surfaces. Once calculated, theexisting UA^(Total) is then parametrically adjusted to quantify newthermal characteristics.

Although comprehensive and customized to a specific building underconsideration, there are notable weaknesses to energy audits. First,energy audits can be quite expensive, costing over a thousand dollarsfor the pre- and post-inspections and the filing of the necessarypaperwork to obtain utility rebates. Second, equipment problems duringtesting can require multiple site visits. Third, energy audit resultsbecome less valid as new energy investments are made, which change thebaseline thermal characteristic findings.

Consider an alternative method. Assume that the original overall thermalcharacteristic UA^(Total) of a building is known. UA^(Total) can bedetermined, for instance, using the empirical approach described suprawith reference to FIG. 4 . Suppose that energy investments are made foronly one portion of the building that only affect heat transfer throughthe building envelope due to conduction. For example, the building owneris considering an investment in new windows, which can be called thej^(th) surface area. The new thermal characteristics of the building

^(Total) equal the original building characteristics UA^(Total), minusthe thermal characteristics of the original windows, plus the thermalcharacteristics of the new windows, which can be expressed as:

^(Total) =UA ^(Total)−(U ^(j) A ^(j) −Û ^(j) A ^(j))=UA ^(Total)−(U ^(j)−Û ^(j))A ^(j)  (39)

where U^(j) and Û^(j) respectively represent the existing and proposedU-values of surface j, and A^(i) represents the surface area of surfacej.

Equation (39) can be restated in a generalized form when there are Minvestments being made in a building:

Total = UA Total + ∑ j = 1 M ( U j - U ^ j ) ⁢ A j ( 40 )

Suppose further that energy investments are made that affect heat lossesdue to infiltration. As discussed supra with reference to Equation (18),infiltration losses are based on the density of air (ρ), specific heatof air (c), number of air changes per hour (n), and volume of air perair change (V). The volume of a building can be approximated bymultiplying building square footage by average ceiling height. Equation(40) can be modified to account for “Before” and “After” infiltrationheat transfer:

Total = UA Total + ∑ j = 1 M ( U j - U ^ j ) ⁢ A j + ρ ⁢ c ⁡ ( n - n ^ ) ⁢ V( 41 )

Substituting Equation (41) into Equation (38):

$\begin{matrix}{{\hat{Q}}^{F - {Heating}} = {(H)( Q^{F} )( {1 - \frac{{\sum\limits_{j = 1}^{M}{( {U^{j} - {\hat{U}}^{j}} )A^{j}}} + {\rho{c( {n - \hat{n}} )}V}}{{UA}^{Total}}} )( \frac{\eta^{furnace}}{{\hat{\eta}}^{furnace}} )( \frac{\eta^{delivery}}{{\hat{\eta}}^{delivery}} )}} & (42)\end{matrix}$

Equation (42) implies that only the following information is required toquantify the energy impact of building envelope investments:

-   -   Percentage of fuel bill used for heating purposes (II), which        can be obtained from monthly fuel bill data.    -   Existing fuel bill (Q^(F)), which can be obtained from the local        utility bill records.    -   Existing overall thermal properties of building (UA^(Total)),        which can be determined using the empirical approach described        supra with reference to FIG. 4 .    -   Existing furnace efficiency (η^(furnace)). This value is based        on manufacturer and furnace model and is often listed directly        on the furnace chassis or manufacturer specifications.    -   New furnace efficiency ({circumflex over (η)}^(furnace)) This        value is based on manufacturer and furnace model and is often        listed directly on the furnace chassis or manufacturer        specifications.    -   Existing delivery system efficiency ({circumflex over        (η)}^(delivery)). This value typically ranges between 70 and 95        percent. η^(delivery) can be estimated or can be measured        directly using a duct blast (or duct leakage) test, which is a        detailed, on-site test. Alternatively, delivery system        efficiency can be measured empirically using temperature tests        in the spaces in which the ducts are located.    -   New delivery system efficiency ({circumflex over        (η)}^(delivery)). This value can be specified as a requirement        as part of ductwork replacement. Verification involves a        detailed, on-site test.    -   Areas of building surfaces to be replaced or upgraded. These        values can be determined using a tape measure and a calculator,        or software.    -   Existing U-values of thermal properties of building surfaces to        be replaced or upgraded. These values can be estimated.    -   New U-values of thermal properties of building surfaces to be        replaced or upgraded. These values are reported by the surface        manufacturer.    -   Number of air changes before and after energy investment. This        number is required for energy investments that affect        infiltration, but not for many other building        envelope-implicating energy investments. Verification involves a        detailed, on-site test.

The foregoing parameters are substituted into Equation (42) (step 193),which is then simplified (step 194) to find the annual cost 196 andpayback 197.

In some special cases, Equation (42) can be simplified to:

$\begin{matrix}{{\hat{Q}}^{F - {Heating}} = {(H)( Q^{F} )( {1 - \frac{( {U^{j} - {\hat{U}}^{j}} )A^{j}}{{UA}^{Total}}} )}} & (43)\end{matrix}$

which applies when the heating source is not being replaced, thedelivery system is not being upgraded, the investment does not affectthe number of air changes per hour, or there is only one investmentunder consideration. Similar to Equation (42), the foregoing parametersare substituted into Equation (43) (step 193), which is then simplified(step 194) to find the annual cost 196 and payback 197.

Consider two examples that show how Equation (43) can be used. In bothexamples, assume that the buildings overall thermal performanceUA^(Total) is 800, the natural gas bill is $1,000 annually, 60 percentof the natural gas consumed is for heating, and that natural gas costs$1 per therm.

Example: A homeowner is considering a $10,000 investment to upgradesingle-pane windows with an R-value of 0.8 to triple-pane, low-e, argongas-filled windows with an R-value of 6.7. The homeowner has 300 ft² ofwindows. How much would the homeowner save on heating?

The homeowner currently purchases 1,000 therms per year of natural gasbased on an annual heating bill of $1,000 and natural gas price of $1per therm. Assuming that 400 therms are for non-heating purposes,leaving 600 therms for heating. According to Equation (43), the newheating fuel consumption will be:

$\begin{matrix}{{\hat{Q}}^{F - {Heating}} = {{(0.6)( {1,000} )( {1 - \frac{( {\frac{1}{0.8} - \frac{1}{6.7}} )300}{800}} )} = {352{therms}}}} & (44)\end{matrix}$

The $10,000 investment will save the homeowner $248 per year($1/therm)×(600 therms−352 therms).

Example: The same homeowner decided to look into a different energyinvestment. The home currently has a 2,500 ft² ceiling with R-6insulation. The homeowner is considering spending $1,000 to upgrade toR-30 insulation. According to Equation (43), the new heating fuelconsumption will be:

$\begin{matrix}{{\hat{Q}}^{F - {Heating}} = {{(0.6)( {1,000} )( {1 - \frac{( {\frac{1}{6} - \frac{1}{30}} )2,500}{800}} )} = {350{therms}}}} & (45)\end{matrix}$

This $1,000 investment will save the homeowner $250 per year($1/therm)×(600 therms−350 therms).

Note that Equation (38), Equation (42), and Equation (43) can all beused in the evaluation of energy investments affecting buildingenvelope, furnace, and heat delivery. Choosing the appropriate equationdepends upon the form of energy investment under consideration. FIG. 21is a process flow diagram showing a routine for selecting energyinvestment scenario parameters 200 for use in the method 190 of FIG. 20. In all three cases, the annual payback 197 on fuel savings for spaceheating from proposed energy investments can be determined. However,depending upon the energy investment, different parameters are requiredand, in some cases, a simpler form of evaluation by choosing an equationrequiring fewer parameters might be used (step 201). If the proposedenergy investments mainly affect heating efficiency or deliveryefficiency (step 202), Equation (38) is the most appropriate form ofevaluation. If the proposed energy investments only affect heat transferdue to conduction through only one portion of a building (step 203),Equation (42) is better suited to the task. Finally, when the heatingsource is not being replaced, the delivery system is not being upgraded,the investment does not affect the number of air changes per hour, orthere is only one investment under consideration (step 204), Equation(43) can be used.

A typical household in California consumes about 6,875 kWh ofelectricity annually. A 4.5 kW-DC photovoltaic power generation systemcan provide enough power generating capacity to meet that level ofconsumption. Electricity, however, is only a part of overall energyconsumption. Providing only net energy consumption data creates amisperception that a home is energy efficient. Gross energy load data ishelpful in dispelling that concern, yet gross energy load remainsprincipally focused on electricity consumption. A holistic view of allforms of energy consumption is more apt to enable a consumer to identifyopportunities to improve energy conservation across-the-board and torealize a zero net energy consumption paradigm, including transportationand denoted by ZNET (Zero Net Energy including Transportation), byspecifically highlighting all forms of energy consumption, whetherelectricity or other energy sources, and the amount of on-site powergeneration required to meet those energy consumption needs. FIG. 22 is ablock diagram depicting, by way of example, annual energy consumption byan average household in California with gasoline and natural gasconsumption expressed in kilowatt hours. The area of the rectangles forthe different forms of energy consumption shown are drawn to scale. Suchenergy consumption modeling could be provided as a trusted energyadvisor tool included through informational Web sites provided by powerutilities or energy agencies to their customers, as well as in printedform.

Here, the 6,875 kWh of annual electricity consumption is viewed inperspective to energy consumed to fulfill personal transportation, waterheating, and space heating needs. Each of these types of energyconsumption can be normalized to kilowatt hours, or other units ofenergy, for purposes of comparison. The 729 gallons of gasoline convertsinto approximately 24,564 kWh, using a conversion of 33.7 kWh per gallonof gasoline. The 219 therms of natural gas (NG) for water heating and238 therms of NG for space heating respectively convert intoapproximately 6,417 kWh and 6,973 kWh, using a conversion of 29.3 kWhper therm of natural gas. The total energy consumption, when thusconsidered, is around 44,829 kWh or about 85% more than annualelectricity consumption alone.

Space heating and simple electricity consumption can be effectivelyreduced through traditional forms of energy efficiency. FIG. 23 is ablock diagram depicting, by way of example, the annual energyconsumption of FIG. 22 reflecting energy efficiencies implementedthrough traditional methodologies. Here, energy consumption for bothspace heating and other electricity have respectively been reduced byaround 40%. Other electricity consumption has been reduced to 4,125 kWhby implementing electricity efficiency measures, which includes cuttingdown on and avoiding wasteful energy use, for instance, turning offunnecessary lights or appliances, and by switching to energy efficientfixtures, such as LED lighting fixtures. Space heating consumption hasbeen reduced to 4,184 kWh by implementing thermal efficiency, whichincludes improving the thermal efficiency and performance of a building,as described supra with reference to FIG. 8 .

Non-traditional forms of energy efficiency are less familiar to mostconsumers, yet can save a significant amount of energy annually. Forinstance, replacing a gasoline-powered vehicle with an electric vehicleis a major energy saver, as well as being instrumental in reducinggreenhouse emissions and other environmental harms. FIG. 24 is a blockdiagram depicting, by way of example, the annual energy consumption ofFIG. 22 reflecting a switch to an electric vehicle. An electric vehiclewill increase electricity consumption due to the need for regularrecharging, yet will also reduce overall energy use. Here, energyconsumption for personal transportation has been reduced to 4,913 kWh byswitching to an electric vehicle, which is about 20% of the energyrequired by a gasoline-powered vehicle.

Another form of non-traditional energy efficiency is fuel switching froma water heater fueled by natural gas to a heat pump water heater. FIG.25 is a block diagram depicting, by way of example, the annual energyconsumption of FIG. 22 reflecting a switch to a heat pump water heater.The annual water heating capacity for the building is first determined,from which an appropriately-sized heat pump water heater can beselected. Here, energy consumption for water heating has been reduced to1,540 kWh by switching to a heat pump water heater of equivalentcapacity as the natural gas unit that was replaced.

The same type of fuel switch can be made for a space heating. FIG. 26 isa block diagram depicting, by way of example, the annual energyconsumption of FIG. 22 reflecting a switch to a heat pump space heater.The annual space heating capacity for the building is first determined,from which an appropriately-sized heat pump space heater can beselected. Here, energy consumption for space heating has been furtherreduced to 1,339 kWh by switching to a heat pump space heater ofequivalent capacity as the natural gas unit that was replaced, resultingin a total energy savings of about 20% of the pre-energy conservationamount of 6,973 kWh.

Total energy savings adds up. FIG. 27 is a block diagram depicting, byway of example, the annual energy consumption of FIG. 22 with cumulativerevised energy consumption expressed in kilowatt hours. With bothtraditional and non-tradition energy efficiencies, annual energyconsumption is about 11,917 kWh, which is nearly a 75% reduction inenergy. To achieve a ZNE household, on-site power generation capacitywould need to be increased. FIG. 28 is a block diagram depicting, by wayof example, the cumulative revised energy consumption of FIG. 27overlaying a 20% efficient photovoltaic power generation system. On-sitepower generation can be simulated for different photovoltaic powergeneration system configurations based on solar irradiance data for aset of locations representative of the geographic region within whichthe building is located, such as described supra with reference to FIG.17 . Here, based on current photovoltaic technology, a solar array witha 20% efficiency rating that takes up only a small portion of a 30 feetby 50 feet roof would generate about 11,917 kWh, which is enough tosatisfy the new energy needs.

Fractionally inferring the percentage of the total fuel purchased forspace heating purposes, as described supra with reference to FIG. 2 ;empirically estimating overall thermal performance of a building througha short-duration controlled test, as described supra with reference toFIG. 4 ; evaluating potential energy investment scenarios, as describedsupra with reference to FIG. 10 ; determining gross energy load, asdescribed supra with reference to FIG. 17 ; and evaluating new energyinvestments specifically affecting building envelope, heating source, orheating delivery, as described supra beginning with reference to FIG. 20, can be performed with the assistance of a computer, or through the useof hardware tailored to the purpose. FIG. 29 is a block diagram showinga computer-implemented system 210 for empirically estimating overallthermal performance of a building through a short-duration controlledtest, in accordance with one embodiment, which can also be used forfractionally inferring the percentage of the total fuel purchased forspace heating purposes and evaluating potential energy investmentscenarios. A computer system 211, such as a personal, notebook, ortablet computer, as well as a smartphone or programmable mobile device,can be programmed to execute software programs 212 that operateautonomously or under user control, as provided through user interfacingmeans, such as a monitor, keyboard, and mouse. The computer system 211includes hardware components conventionally found in a general purposeprogrammable computing device, such as a central processing unit,memory, input/output ports, network interface, and non-volatile storage,and execute the software programs 212, as structured into routines,functions, and modules. In addition, other configurations ofcomputational resources, whether provided as a dedicated system orarranged in client-server or peer-to-peer topologies, and includingunitary or distributed processing, communications, storage, and userinterfacing, are possible.

The computer system 211 remotely interfaces to a heating source 216 anda thermometer 217 inside a building 213 that is being analyticallyevaluated for overall thermal performance UA^(Total). In a furtherembodiment, the computer system 211 also remotely interfaces to athermometer 218 outside the building 213, or to a remote data sourcethat can provide the outdoor temperature. The computer system 211 cancontrol the heating source 216 and read temperature measurements fromthe thermometer 217 throughout the short-duration controlled test,during which the baseline indoor temperature T₀, the starting indoortemperature T₁, and the final indoor temperature T₃ are recorded. In afurther embodiment, a cooling source (not shown) can be used in place ofor in addition to the heating source 216. The expected final indoortemperature T₃ ^(No Heat) is also estimated by the computer system 211,based on a projection of what the indoor temperature would have been atthe end of the test, had the heating source not been turned back on. Thecomputer system 211 executes a software program 212 to determine overallthermal performance UA^(Total) based on the empirical approach describedsupra with reference to FIG. 4 .

In a further embodiment, the computer system 211 may be remotelyinterfaced with a server 220 operated by a power utility or otherutility service provider 221 over a wide area network 219, such as theInternet, from which fuel purchase data 222, as well as period netconsumption statistics, can be retrieved. The computer system 211executes a software program 212 to fractionally infer the percentage ofthe total fuel purchased for space heating purposes, as described suprawith reference to FIG. 4 , and also to determine gross energy load, asdescribed supra with reference to FIG. 17 .

In a still further embodiment, the UA^(Total) can be used as part of thebuilding thermal characteristics. Optionally, the computer system 211may also monitor electricity 214 and other metered fuel consumption,where the meter is able to externally interface to a remote machine, aswell as monitor on-site power generation, such as generated by aphotovoltaic system 215. The monitored fuel consumption and powergeneration data can be used to create the electricity, fuel, andgasoline consumption data 96 and historical solar resource and weatherdata 98. The computer system 211 executes a software program 212 toevaluate potential energy investment scenarios, and provide a paybackestimate 217, as described supra with reference to FIG. 10 .

In a yet further embodiment, the computer system 211 includes a storagedevice within which is stored one or more of the following data: thepercentage of fuel bill used for heating purposes, an existing fuelbill, existing overall thermal properties UA^(Total) of the building213, existing furnace efficiency, new furnace efficiency, existingdelivery system efficiency, new delivery system efficiency, areas ofbuilding surfaces to be replaced or upgraded, existing U-values ofthermal properties of building surfaces to be replaced or upgraded, newU-values of thermal properties of building surfaces to be replaced orupgraded, and number of air changes before and after energy investment.The computer system 211 executes a software program 212 to evaluate newenergy investments specifically affecting building envelope, heatingsource, or heating delivery, and provide a payback estimate 187, asdescribed supra with reference to FIG. 20 .

While the invention has been particularly shown and described asreferenced to the embodiments thereof, those skilled in the art willunderstand that the foregoing and other changes in form and detail maybe made therein without departing from the spirit and scope.

1. A system for building heating-modification-based gross energy loadmodification modeling with the aid of a digital computer, comprising: acomputer comprising a processor and memory within which code forexecution by the processor is stored, the computer configured to: obtaina gross energy load associated with a building based on electricityprovided to the building by a power utility and energy provided to thebuilding by an on-site renewable energy system; estimate an overallthermal performance of the building by conducting an empirical testcomprising remotely controlling a heating source inside the building;model an effect of one or more changes to the overall thermalperformance of the building on the gross energy load comprisingdetermining a characteristic of a further heating source needed tosupply heat for space heating the building with the changed overallthermal performance, determining the characteristic of the furtherheating source comprising: obtaining a maximum amount of energy consumedin a single day during a time period for space heating in the building;determining at least one mathematical relationship between heatinglosses in the building before the changes are performed and estimatedheating losses to be in the building after the changes are performed,and use the at least one mathematical relationship and the maximumamount of energy to determine a further maximum amount of the energythat would be needed in the building in a single day after the changesare performed; determine the characteristic based on the further maximumamount of the energy needed in the building after the changes areperformed; and determine a characteristic of a further renewable energysystem needed to power the further heating source using thecharacteristic of the heating source.
 2. A system according to claim 1,wherein the heating losses comprise envelope heating losses and ductheating losses and the estimated heating losses comprise estimatedenvelope heating losses and estimated duct heating losses.
 3. A systemaccording to claim 2, the computer further configured to determine aratio of the envelope heating losses and the estimated envelope heatinglosses and a ratio of the duct heating losses and the estimated ductlosses.
 4. A system according to claim 3, the computer furtherconfigured to determine a product of the ratios, wherein themathematical relationship comprises the product of the ratios.
 5. Asystem according to claim 1, wherein the time period is one year.
 6. Asystem according to claim 1, wherein the further heating source replacesa gas heating source.
 7. A system according to claim 6, furthercomprising: obtain the amounts of natural gas purchased during aplurality of days during the time period for the building; and use theamounts of the natural gas to determine the maximum amount of energy. 8.A system according to claim 6, the computer further configured to obtainan efficiency of the natural gas heating source and the further heatingsource and to use the efficiencies to determine the characteristic.
 9. Asystem according to claim 6, the computer further configured to obtain anumber of hours during the natural gas heating source operated and amaximum number of hours in a further day the further heating source willoperate and to use the maximum numbers of hours in calculating thecharacteristic.
 10. A system according to claim 6, the computer furtherconfigured to calculate a cost associated with replacing the natural gasheating source with the further heating source using the characteristic.11. A method for building heating-modification-based gross energy loadmodification modeling with the aid of a digital computer, comprising:obtaining by a computer, the computer comprising a processor and memorywithin which code for execution by the processor is stored, a grossenergy load associated with a building based on electricity provided tothe building by a power utility and energy provided to the building byan on-site renewable energy system; estimating by the computer anoverall thermal performance of the building by conducting an empiricaltest comprising remotely controlling a heating source inside thebuilding; modeling by the computer an effect of one or more changes tothe overall thermal performance of the building on the gross energy loadcomprising determining a characteristic of a further heating sourceneeded to supply heat for space heating the building with the changedoverall thermal performance, determining the characteristic of thefurther heating source comprising: obtaining a maximum amount of energyconsumed in a single day during a time period for space heating in thebuilding; determining at least one mathematical relationship betweenheating losses in the building before the changes are performed andestimated heating losses to be in the building after the changes areperformed, and use the at least one mathematical relationship and themaximum amount of energy to determine a further maximum amount of theenergy that would be needed in the building in a single day after thechanges are performed; determining by the computer the characteristicbased on the further maximum amount of the energy needed in the buildingafter the changes are performed; and determining by the computer acharacteristic of a further renewable energy system needed to power thefurther heating source using the characteristic of the heating source.12. A method according to claim 11, wherein the heating losses compriseenvelope heating losses and duct heating losses and the estimatedheating losses comprise estimated envelope heating losses and estimatedduct heating losses.
 13. A method according to claim 12, furthercomprising determining a ratio of the envelope heating losses and theestimated envelope heating losses and a ratio of the duct heating lossesand the estimated duct losses.
 14. A method according to claim 13,further comprising determining a product of the ratios, wherein themathematical relationship comprises the product of the ratios.
 15. Amethod according to claim 11, wherein the time period is one year.
 16. Amethod according to claim 11, wherein the further heating sourcereplaces a gas heating source.
 17. A method according to claim 16,further comprising: obtaining the amounts of natural gas purchasedduring a plurality of days during the time period for the building; andusing the amounts of the natural gas to determine the maximum amount ofenergy.
 18. A method according to claim 16, further comprising obtainingan efficiency of the natural gas heating source and the further heatingsource and using the efficiencies to determine the characteristic.
 19. Amethod according to claim 16, further comprising obtaining a number ofhours during the natural gas heating source operated and a maximumnumber of hours in a further day the further heating source will operateand using the maximum numbers of hours in calculating thecharacteristic.
 20. A method according to claim 16, further comprisingcalculating a cost associated with replacing the natural gas heatingsource with the further heating source using the characteristic.